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:
33 = 27
Express the following in the logarithmic form:
54 = 625
Express the following in the logarithmic form:
90 = 1
Express the following in the logarithmic form:
`(1)/(8)` = 2-3
Express the following in the logarithmic form:
112 = 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:
70 = 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:
log2 128 = 7
Express the following in the exponential form:
log3 81 = 4
Express the following in the exponential form:
log10 0.001 = -3
Express the following in the exponential form:
`"log"_2 (1)/(32)` = -5
Express the following in the exponential form:
logb a = c
Express the following in the exponential form:
`"log"_2 (1)/(2)` = -1
Express the following in the exponential form:
log5 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 = loga p
Express the following in the exponential form:
`"log"_sqrt(6) (6sqrt(6))` = 3
Express the following in the exponential form:
-2 = log2 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 0.0110
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 a3
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: 102a -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 : 10p
If log 10 x = p, express the following in terms of x: 10p+1
If log 10 x = p, express the following in terms of x: 102p-3
If log 10 x = p, express the following in terms of x: 102-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
102x-3 in term of a
If Iog 10 a = x, log 10 b = y and log 10 c = z, find
103y -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 102 = 100
True
False
State true or false in the following:
If log 10 p = q, then 10p = q
True
False
State true or false in the following:
If 43 = 64, then log 3 64 = 4
True
False
State true or false in the following:
If xy = z, then y = logxz
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: log128
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(x2 + 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 (x2 - 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 log103 + 1 in terms of log10x.
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:
logba =-logab
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
10a-1 in terms of x
If log x = a and log y = b, write down
102b in terms of y
If log 3 m = x and log 3 n = y, write down
32x-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 log1025 = x and log1027 = y; evaluate without using logarithmic tables, in terms of x and y: log105
If log1025 = x and log1027 = y; evaluate without using logarithmic tables, in terms of x and y: log103
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 x2 + y2 = 6xy, prove that `"log"((x - y)/2) = (1)/(2)` (log x + log y)
If x2 + y2 = 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 x2 - 8)
If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.
Simplify: log a2 + log a-1
Simplify: log b ÷ log b2
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 5a+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 ba.ab = 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 + logp 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.
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