B Nirmala Shastry solutions for मॅथेमॅटिक्स [अंग्रेजी] कक्षा ९ आयसीएसई chapter 7 - Logarithms [Latest edition]

Express the following in logarithmic form.

4² = 16

Express the following in logarithmic form.

7³ = 343

Express the following in logarithmic form:

`3^-2 = 1/9`

Express the following in logarithmic form.

6⁰ = 1

Express the following in logarithmic form.

`36^(1/2) = 6`

Express the following in logarithmic form:
10^–3 = 0.001

Express the following in logarithmic form.

`25 = 125^(2/3)`

Change the following into exponent form.

log₃ 81 = 4

Change the following into exponent form.

log₅ 25 = 2

Change the following into exponent form.

`log_27 81 = 4/3`

Change the following into exponent form.

`log_2  1/4 = -2`

Change the following into exponent form.

`log_5  1/125 = -3`

Change the following into exponent form.

log₁₀ 0.01 = –2

Find the value of log₄ 64.

Find the value of log₂ 16.

Find the value of `log_3  1/9`.

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

Find the value of `log_(1/10) 100`.

Find the value of `log_4  1/64`.

Find the value of x in the following:

log_x 16 = 4

Find the value of x in the following:

`log_x  1/27 = 3`

Find the value of x in the following:

`log_x  1/343 = -3`

Find the value of x in the following:

log_x 0.1 = –1

Find the value of x in the following:

log_x 8 = 6

Find the value of x in the following:

`log_x 10 = 1/2`

Find the value of x in the following:

`log_(sqrt(3)) (x + 2) = 2`

Find the value of x in the following:

`log_(sqrt(5))(x + 8) = 4`

Find the value of x in the following:

log₃ (x² – 19) = 4

If log₁₀ a = m, express the following in terms of a.

10^3m

If log₁₀ a = m, express the following in terms of a.

10^{m + 2}

If log₁₀ a = m, express the following in terms of a.

10^5m−3

If log₁₀ x = m, log₁₀ y = n, write 10^{3m + 1} in terms of x.

If log₁₀ x = m, log₁₀ y = n, write 10^{2n – 3} in terms of y.

If log₁₀ x = m, log₁₀ y = n, write xy in terms of m and n.

If log₁₀ x = m, log₁₀ y = n, write `x/y` in terms of m and n.

Given log₁₀ a = m, log₁₀ b = n, log₁₀ c = p, express k in terms of a, b and c if k = 10^{2m + 3n – 5p}.

If log₅ a = 2, log₃ b = 3, find the value of 3a – 2b.

Express as a single logarithm:

log 3 + log 4 + log 5

Express as a single logarithm:

`log 2 - 1/3 log 125 + 1/4 log 81`

Express as a single logarithm:

`2 log 3 - 1/2 log 4 + 1/3 log 64`

Express as a single logarithm:

`1/2 log 36 + 2 log 5 - 3 log 2`

Express as a single logarithm:

1 + log 4 – log 5

Express as a single logarithm:

`2 + 1/3 log 8 - 2 log 5`

Express as a single logarithm:

3 – 2 log 5 + 3 log 2

Express as a single logarithm:

`2/3 log 8 + 6 log root(3)(2) - 1/2 log  1/9`

Evaluate the following:

`log 8 + 2 log 5 - 1/3 log 8`

Evaluate the following:

4 log 2 + 3 log 5 – log 2

Evaluate the following:

`1/2 log 25 + log 4 - 1/3 log 8`

Evaluate the following:

`2 log 6 - 2 log 3 + 1/2 log 625`

Evaluate the following:

1 + 3 log 5 + 3 log 2

Evaluate the following:

`log  3/4 + log  4/5 + log  5/6 - log  1/2`

Evaluate the following:

`log  81/8 + 2 log  2/3 - 3 log  3/2 + log  3/4`

Solve for x:

log (x + 6) + log (x – 6) = 2 log 8

Solve for x:

log (2x – 3) + log 3 = log (2x + 7)

Solve for x:

log (x – 5) + log 4 = 2

Solve for x:

log (x + 3) + log (x – 3) = 3 log 2 + log 5

Solve for x:

log (x – 6) + log (x – 3) = 2 log 2

Solve for x:

log 2x + log 6 = 1 + log 12

Solve for x:

log (x + 3) + log (x – 5) = 2 log 3

Solve for x:

log (3x + 5) – log (x – 3) = 1

Solve for x:

log (5x + 6) + log (5x – 6) = 2 log 8

Solve for x:

log (7x + 3) – log (x – 3) = 1

Express V in terms of other quantities in the following:

log V + log 3 = log 2 + log π + 3 log r

Express P in terms of others:

log P + log T = 2 log 10 + log I – log R

Express A in terms of others:

2 log A – log S = log (S – a) + log (S – b) + log (S – c)

Solve for x:

log_x4 = 2 – log_x9

If a = 1 + log 2 – log 5, b = 2 log 3 and c = log m – log 5, find the value of m if a + b = 2c.

Given log 2 = a, log 3 = b, express the following in terms of a or b or both.

log 1.5

Given log 2 = a, log 3 = b, express the following in terms of a or b or both.

log 1.2

Given log 2 = a, log 3 = b, express the following in terms of a or b or both.

log 0.24

Given log 2 = a, log 3 = b, express the following in terms of a or b or both.

log 0.5

Given log 2 = a, log 3 = b, express the following in terms of a or b or both.

log 0.036

Given log 9 = a, express log 300 and `log sqrt(0.009)` in terms of a.

If log 8 = 0.9030, express the following:

log 64

If log 8 = 0.9030, express the following:

log 2000

If log 8 = 0.9030, express the following:

`log  5/4`

If log 8 = 0.9030, express the following:

log 4

Simplify the following:

`log 625/log 5`

Simplify the following:

`log 8/log 4`

Simplify the following:

`log 216/log 6`

Simplify the following:

`log sqrt(343)/log 49`

Simplify the following:

`log sqrt(32)/log 8`

Express a in terms of b in the following:

`1/2 log a + 5 log b = 1`

Express a in terms of b in the following:

`2 log a - 1/3 log b = 2`

`log_2  1/8 = x`,

∴ The value of x is ______.

`log_sqrt(5) (x + 3) = 2`

∴ The value of x is ______.

If log₁₀ a = m, then 10^3m+1 in terms of a is ______.

25 = 5² in log form is ______.

log₃ b = 4.

∴ The value of b is ______.

`log 8/log 4` = ______

2 log 2 – 3 log 3 + 4 log 4 = ______

log(x + 3) + log(x – 3) = 4 log 2.

∴ The value of x is ______.

log (x – 5) + log 2 = 1.

∴ The value of x is ______.

log (3x + 1) – log (x – 2) = 1.

∴ x = ______

If log 2 = x, log 3 = y. Then log 6 = ______.

If log 7 = x then log 700 = ______.

If log 125 + log 8 = x then the value of x is ______.

Assertion: If log₁₀ a = x then 10^x+2 = 100a.

Reason: 10^x+2 = 10^x × 10² = 100 × 10^x.

Assertion: If log 2 = a, log 3 = b then log 6 = ab.

Reason: log 6 = log 2 + log 3.

Assertion: If log 80 = a then `log 2 = (a - 1)/3`.

Reason: log 8 = 3 log 2.

Assertion: If log (3x – 5) = 1, then x = 2

Reason: If a^m = n, then log_a n = m

Assertion: If log 5 = m, then log 500 = 100 + m

Reason: log ab = log a + log b

Assertion: `2 log 3 - 1/2 log 4 + 3 log 2 = log 36`

Reason: `log a - log b + log c = log  a/(bc)`

Find the value of x:

`log_sqrt(3) (x - 1) = 2`

Find the value of x:

log₅ (x² + 9) = 2

Find the value of x:

log_x 8 = 2 – log_x 18

Evaluate:

`log_3  1/27`

Evaluate:

log₁₀ 0.001

Evaluate:

log_a a

Express as single log:

`1/3 log 125 - 2 log 3 + 1/4 log 625`

Solve for x:

log (4x – 3) + log (4x + 3) = 4 log 2

Solve for x:

log (10x + 5) – log (x – 4) = 2

Solve for x:

`2 log x + 1/3 log 125x^3 = 3 log 2 + log 5`

Express V in terms of other quantities in the following:

log V + log 3 = log π + 2 log r + log h

Simplify the following:

`logsqrt(125)/log25`

Simplify the following:

`log 64/log 32`

Given log 2 = a, log 3 = b, express in terms of a and b.

log 6

Given log 2 = a, log 3 = b, express in terms of a and b.

log 4.8

Given log 2 = a, log 3 = b, express in terms of a and b.

log 125

If log₁₀ a = m, log₁₀ b = n and K = 10^{5m – 4n}, express K in terms of a and b.

Given `1/4 log a^3  +  5 log sqrt(b) = 1`, find the value of a³b¹⁰.

Find the value of x:

`log_sqrt(5) (log_3x) = 2`

If log 9 = 0.9542, find the value of log 30.

If log 9 = 0.9542, find the value of log 27.

If log 2 = 0.3010, log 3 = 0.4771 and log 7 = 0.8451, find the value of log 84.

If log 2 = 0.3010, log 3 = 0.4771 and log 7 = 0.8451, find the value of `log 1 1/6`.