#### Chapters

Chapter 2: Profit , Loss and Discount

Chapter 3: Compound Interest

Chapter 4: Expansions

Chapter 5: Factorisation

Chapter 6: Changing the subject of a formula

Chapter 7: Linear Equations

Chapter 8: Simultaneous Linear Equations

Chapter 9: Indices

Chapter 10: Logarithms

Chapter 11: Triangles and their congruency

Chapter 12: Isosceles Triangle

Chapter 13: Inequalities in Triangles

Chapter 14: Constructions of Triangles

Chapter 15: Mid-point and Intercept Theorems

Chapter 16: Similarity

Chapter 17: Pythagoras Theorem

Chapter 18: Rectilinear Figures

Chapter 19: Quadrilaterals

Chapter 20: Constructions of Quadrilaterals

Chapter 21: Areas Theorems on Parallelograms

Chapter 22: Statistics

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Perimeter and Area

Chapter 25: Surface Areas and Volume of Solids

Chapter 26: Trigonometrical Ratios

Chapter 27: Trigonometrical Ratios of Standard Angles

Chapter 28: Coordinate Geometry

## Chapter 10: Logarithms

### Frank solutions for Class 9 Maths ICSE Chapter 10 Logarithms Exercise 10.1

Express the following in the logarithmic form:

3^{3} = 27

Express the following in the logarithmic form:

5^{4} = 625

Express the following in the logarithmic form:

9^{0} = 1

Express the following in the logarithmic form:

`(1)/(8)` = 2^{-3}

Express the following in the logarithmic form:

11^{2} = 121

Express the following in the logarithmic form:

3^{-2} = `(1)/(9)`

Express the following in the logarithmic form:

10^{-4} = 0.0001

Express the following in the logarithmic form:

7^{0} = 1

Express the following in the logarithmic form:

`(1/3)^4 = (1)/(81)`

Express the following in the logarithmic form:

9^{-4} = `(1)/(6561)`

Express the following in the exponential form:

log_{2} 128 = 7

Express the following in the exponential form:

log_{3} 81 = 4

Express the following in the exponential form:

log_{10} 0.001 = -3

Express the following in the exponential form:

`"log"_2 (1)/(32)` = -5

Express the following in the exponential form:

log_{b} a = c

Express the following in the exponential form:

`"log"_2 (1)/(2)` = -1

Express the following in the exponential form:

log_{5} a = 3

Express the following in the exponential form:

`"log"_sqrt(3)` 27 = 6

Express the following in the exponential form:

`"log"_25 sqrt(5) = (1)/(4)`

Express the following in the exponential form:

q = log_{a} p

Express the following in the exponential form:

`"log"_sqrt(6) (6sqrt(6))` = 3

Express the following in the exponential form:

-2 = log_{2} 0.25

Find x in the following when: log _{x} 49 = 2

Find x in the following when: log_{ x} 125 = 3

Find x in the following when: log _{x} 243 = 5

Find x in the following when: log _{8} x = `(2)/(3)`

Find x in the following when: log _{7} x = 3

Find x in the following when: log _{4} x = -4

Find x in the following when: log _{2} 0.5 = x

Find x in the following when: log _{3} 243 = x

Find x in the following when: log _{10} 0.0001 = x

Find x in the following when: log _{4} 0.0625 = x

Find the value of: log _{10} 1000

Find the value of: log _{3} 81

Find the value of: log _{5} 3125

Find the value of: log _{2 }128

Find the value of: `"log" _(1/5) 125` = x

Find the value of: log _{10} 0.0001

Find the value of: log _{5} 125

Find the value of: log _{8} 2

Find the value of: `"log_(1/2)16`

Find the value of: log _{0.01}10

Find the value of: log _{3} 81

Find the value of: log _{5 }`(1)/(25)`

Find the value of: log _{2} 8

Find the value of: log _{a }a^{3}

Find the value of: log _{0.1} 10

Find the value of: `"log_sqrt(3) (3sqrt(3))`

If log _{10} x = a, express the following in terms of x : 10 ^{2a}

If log _{10} x = a, express the following in terms of x: 10 ^{a + 3}

If log _{10} x = a, express the following in terms of x: 10 ^{-a}

If log _{10} x = a, express the following in terms of x: 10^{2a -3}

If log _{10} m = n, express the following in terms of m: 10^{ n -1}

If log _{10} m = n, express the following in terms of m: 10 ^{2n+1 }

If log _{10} m = n, express the following in terms of m: 10 ^{-3n}

If log _{10 }x = p, express the following in terms of x : 10^{p}

If log _{10 }x = p, express the following in terms of x: 10^{p+1 }

If log _{10} x = p, express the following in terms of x: 10^{2p-3}

If log _{10} x = p, express the following in terms of x: 10^{2-p}

If log _{10} x = a, log _{10} y = b and log _{10} z = 2a - 3b, express z in terms of x and y.

If Iog _{10 }a = x, log_{ 10} b = y and log _{10} c = z, find

10^{2x-3 }in term of a

If Iog _{10 }a = x, log_{ 10} b = y and log _{10} c = z, find

10^{3y -1} in terms of b

If log _{10} a = x, and log _{10} c = z, find

`10^(x-y+z)` in terms of a, b and c

State true or false in the following:

If log _{10} 100 = 2, then 10^{2} = 100

True

False

State true or false in the following:

If log _{10} p = q, then 10^{p} = q

True

False

State true or false in the following:

If 4^{3} = 64, then log _{3} 64 = 4

True

False

State true or false in the following:

If x^{y} = z, then y = log_{x}z

True

False

State true or false in the following:

If log _{2} 8 = 3, then log _{8} 2 = `(1)/(3)`

True

False

### Frank solutions for Class 9 Maths ICSE Chapter 10 Logarithms Exercise 10.2

Express the following in terms of log 2 and log 3: log 36

Express the following in terms of log 2 and log 3: log 54

Express the following in terms of log 2 and log 3: log 144

Express the following in terms of log 2 and log 3: log 216

Express the following in terms of log 2 and log 3: log 648

Express the following in terms of log 2 and log 3: log12^{8}

Express the following in terms of log 5 and/or log 2: log20

Express the following in terms of log 5 and/or log 2: log80

Express the following in terms of log 5 and/or log 2: log125

Express the following in terms of log 5 and/or log 2: log160

Express the following in terms of log 5 and/or log 2: log500

Express the following in terms of log 5 and/or log 2: log250

Express the following in terms of log 2 and log 3: `"log" root(3)(144)`

Express the following in terms of log 2 and log 3: `"log"root(5)(216)`

Express the following in terms of log 2 and log 3: `"log" root(4)(648)`

Express the following in terms of log 2 and log 3: `"log"(26)/(51) - "log"(91)/(119)`

Express the following in terms of log 2 and log 3: `"log"(225)/(16) - 2"log"(5)/(9) + "log"(2/3)^5`

Write the logarithmic equation for:

F = `"G"("m"_1"m"_2)/"d"^2`

Write the logarithmic equation for:

E = `(1)/(2)"m v"^2`

Write the logarithmic equation for:

n = `sqrt(("M"."g")/("m".l)`

Write the logarithmic equation for:

V = `(4)/(3)pi"r"^3`

Write the logarithmic equation for:

V = `(1)/("D"l) sqrt("T"/(pi"r")`

Express the following as a single logarithm:

log 18 + log 25 - log 30

Express the following as a single logarithm:

log 144 - log 72 + log 150 - log 50

Express the following as a single logarithm:

`2 "log" 3 - (1)/(2) "log" 16 + "log" 12`

Express the following as a single logarithm:

`2 + 1/2 "log" 9 - 2 "log" 5`

Express the following as a single logarithm:

`2"log"(9)/(5) - 3"log"(3)/(5) + "log"(16)/(20)`

Express the following as a single logarithm:

`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`

Express the following as a single logarithm:

`2"log" (16)/(25) - 3 "log" (8)/(5) + "log" 90`

Express the following as a single logarithm:

`(1)/(2)"log"25 - 2"log"3 + "log"36`

Express the following as a single logarithm:

`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`

Express the following as a single logarithm:

`3"log"(5)/(8) + 2"log"(8)/(15) - (1)/(2)"log"(25)/(81) + 3`

Simplify the following:

`2 "log" 5 +"log" 8 - (1)/(2) "log" 4`

Simplify the following:

`2"log" 7 + 3 "log" 5 - "log"(49)/(8)`

Simplify the following:

`3"log" (32)/(27) + 5 "log"(125)/(24) - 3"log" (625)/(243) + "log" (2)/(75)`

Simplify the following:

`12"log" (3)/(2) + 7 "log" (125)/(27) - 5 "log" (25)/(36) - 7 "log" 25 + "log" (16)/(3)`

Solve the following:

log (3 - x) - log (x - 3) = 1

Solve the following:

log(x^{2 }+ 36) - 2log x = 1

Solve the following:

log 7 + log (3x - 2) = log (x + 3) + 1

Solve the following:

log ( x + 1) + log ( x - 1) = log 11 + 2 log 3

Solve the following:

log _{4} x + log_{ 4 }(x-6) = 2

Solve the following:

log _{8} (x^{2 }- 1) - log _{8} (3x + 9) = 0

Solve the following:

log (x + 1) + log (x - 1) = log 48

Solve the following:

`log_2x + log_4x + log_16x = (21)/(4)`

Solve for x: log (x + 5) = 1

Solve for x: `("log"27)/("log"243)` = x

Solve for x: `("log"81)/("log"9)` = x

Solve for x: `("log"121)/("log"11)` = logx

Solve for x: `("log"125)/("log"5)` = logx

Solve for x: `("log"128)/("log"32)` = x

Solve for x: `("log"1331)/("log"11)` = logx

Solve for x: `("log"289)/("log"17)` = logx

Express log_{10}3 + 1 in terms of log_{10}x.

State, true of false:

log (x + y) = log xy

True

False

State, true of false:

log 4 x log 1 = 0

True

False

State, true of false:

log_{b}a =-log_{a}b

True

False

State, true of false:

If `("log"49)/("log"7)` = log y, then y = 100.

True

False

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 12

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 75

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 720

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: log 2.25

If log 16 = a, log 9 = b and log 5 = c, evaluate the following in terms of a, b, c: `"log"2(1)/(4)`

If log x = p + q and log y = p - q, find the value of log `(10x)/y^2` in terms of p and q.

If log a = p and log b = q, express `"a"^3/"b"^2` in terms of p and q.

If log x = A + B and log y = A-B, express the value of `"log" x^2/(10y)` in terms of A and B.

If log x = a and log y = b, write down

10^{a-1} in terms of x

If log x = a and log y = b, write down

10^{2b} in terms of y

If log _{3} m = x and log_{ 3} n = y, write down

3^{2x-3} in terms of m

If log _{3} m = x and log_{ 3} n = y, write down

`3^(1-2y+3x)` in terms of m an n

If 2 log x + 1 = 40, find: x

If 2 log x + 1 = 40, find: log 5x

If log_{10}25 = x and log_{10}27 = y; evaluate without using logarithmic tables, in terms of x and y: log_{10}5

If log_{10}25 = x and log_{10}27 = y; evaluate without using logarithmic tables, in terms of x and y: log_{10}3

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log18

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log45

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: log540

If log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990, find the values of: `"log" sqrt(72)`

If 2 log y - log x - 3 = 0, express x in terms of y.

If log 2 = x and log 3 = y, find the value of each of the following on terms of x and y: log60

If log 2 = x and log 3 = y, find the value of each of the following on terms of x and y: log1.2

If log 4 = 0.6020, find the value of each of the following: log8

If log 4 = 0.6020, find the value of each of the following: log2.5

If log 8 = 0.90, find the value of each of the following: log4

If log 8 = 0.90, find the value of each of the following: `"log"sqrt(32)`

If log 27 = 1.431, find the value of the following: log 9

If log 27 = 1.431, find the value of the following: log300

If x^{2} + y^{2} = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)

If x^{2} + y^{2} = 7xy, prove that `"log"((x - y)/3) = (1)/(2)` (log x + log y)

Find x and y, if `("log"x)/("log"5) = ("log"36)/("log"6) = ("log"64)/("log"y)`

If `"log" x^2 - "log"sqrt(y)` = 1, express y in terms of x. Hence find y when x = 2.

If 2 log x + 1 = log 360, find: x

If 2 log x + 1 = log 360, find: log(2 x -2)

If 2 log x + 1 = log 360, find: log (3 x^{2} - 8)

If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.

Simplify: log a^{2} + log a^{-1}

Simplify: log b ÷ log b^{2}

Find the value of:

`("log"sqrt(8))/(8)`

Find the value of:

`("log"sqrt(27) + "log"8 + "log"sqrt(1000))/("log"120)`

Find the value of:

`("log"sqrt125 - "log"sqrt(27) - "log"sqrt(8))/("log"6 - "log"5)`

If a = `"log" 3/5, "b" = "log" 5/4 and "c" = 2 "log" sqrt(3/4`, prove that 5^{a+b-c} = 1

Express the following in a form free from logarithm:

3 log x - 2 log y = 2

Express the following in a form free from logarithm:

2 log x + 3 log y = log a

Express the following in a form free from logarithm:

m log x - n log y = 2 log 5

Express the following in a form free from logarithm:

`2"log" x + 1/2"log" y` = 1

Express the following in a form free from logarithm:

5 log m - 1 = 3 log n

Prove that log (1 + 2 + 3) = log 1 + log 2 + log 3. Is it true for any three numbers x, y, z?

Prove that (log a)^{2} - (log b)^{2} = `"log"("a"/"b")."log"("ab")`

If a b + b log a - 1 = 0, then prove that b^{a}.a^{b} = 10

If log (a + 1) = log (4a - 3) - log 3; find a.

Prove that log _{10 }125 = 3 (1 - log _{10} 2)

Prove that `("log"_"p" x)/("log"_"pq" x)` = 1 + log_{p} q

Prove that: `(1)/("log"_2 30) + (1)/("log"_3 30) + (1)/("log"_5 30)` = 1

Prove that: `(1)/("log"_8 36) + (1)/("log"_9 36) + (1)/("log"_18 36)` = 2

If `"a" = "log""p"^2/"qr", "b" = "log""q"^2/"rp", "c" = "log""r"^2/"pq"`, find the value of a + b + c.

If a = log 20 b = log 25 and 2 log (p - 4) = 2a - b, find the value of 'p'.

## Chapter 10: Logarithms

## Frank solutions for Class 9 Maths ICSE chapter 10 - Logarithms

Frank solutions for Class 9 Maths ICSE chapter 10 (Logarithms) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Class 9 Maths ICSE solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Frank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Maths ICSE chapter 10 Logarithms are Introduction of Logarithms, Interchanging Logarithmic and Exponential Forms, Laws of Logarithm, Expansion of Expressions with the Help of Laws of Logarithm, More About Logarithm, Logarithmic to Exponential, Exponential to Logarithmic, Quotient Law, Power Law, Product Law.

Using Frank Class 9 solutions Logarithms exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 9 prefer Frank Textbook Solutions to score more in exam.

Get the free view of chapter 10 Logarithms Class 9 extra questions for Class 9 Maths ICSE and can use Shaalaa.com to keep it handy for your exam preparation