Question

log 10 base x=log216/log36

Answer 1

$log_{x}(10) = \frac{ log(216) }{ log(36) }$
log a/log b= log a base b
$log_{x}(10) = log_{36}(216)$
36=6^2
216=6^3
$log_{x}(10) = \frac{3}{2} log_{6}(6)$
$log_{x}(10) = \frac{3}{2}$
${x}^{ \frac{3}{2} } = 10$
${x}^{ \frac{3}{2} \times \frac{2}{3} } = {10}^{ \frac{2}{3} }$

$x = \sqrt[3]{100}$

Answer 2

Concept

The laws for logarithmic function are

Product rule:

log(MN) = logM + logN

Quotient rule:

log(M/N) = logM - logN

Power Rule Law:

IogM^n = n IogM

Given

log 10 base x=log216/log36 is given

Find

We need to find the value of x

Solution

log 10 base x=log216/log36

log 10/log x = log 6^3 / log 6^2

log 10/log x = 3 log 6/ 2 log 6

log 10/log x = 3/2

log x/log 10 = 2/3

log x =2/3 log 10

log x = log (10^(2/3))

x = 10^(2/3)

Hence the value of x is 10^(2/3)

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