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If log x 5=a ...

Question

If $l o g_{x} 5 = a$ and $l o g_{20} x = b$ . Then what is the value of $l o g_{x} 10$ ?

A

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B

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C

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Solution

The correct option is A

$l o g_{x} 5 = a$

$l o g_{20} x = b$

$l o g_{5} x = \frac{1}{a}$

$l o g_{20} x = \frac{1}{b}$

$l o g_{x} \frac{100}{5} = \frac{1}{b}$

$l o g_{x} 100 - l o g_{x} 5 = \frac{1}{b}$

$l o g_{x} 100 - \frac{1}{a} = \frac{1}{b}$

$l o g_{x} 10 = \frac{1}{2} (\frac{1}{a} + \frac{1}{b})$

$l o g_{x} 10 = \frac{a + b}{2 a b}$

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Similar questions

If log_x5=a and log₂₀x=b then find the value of log_x10.

{log}_{x} 2 = a, {log}_{x} 3 = b, {log}_{x} 5 = c

then find the value of the following in terms of

a, b

c

{log}_{x} 16

{log}_{x} 75

{log}_{x} 60

{log}_{x} 2 = a, {log}_{x} 3 = b, {log}_{x} 5 = c,

then find the value of the following in terms of a, b, and c,
(i)

{log}_{x} 16

{log}_{x} 75

{log}_{x} 60

{log}_{k} x . {log}_{5} k = {log}_{x} 5, k \neq 1, k > 0

, then the value of

x

\frac{1}{{log}_{x} 10} = \frac{3}{l o g_{p} 10} - 3

x =

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