Question

HeYa

Answer this with step by step explanation​

Answer 1

${16} \: ^{log3} = \: x$

Taking log both sides.

$log(16 {} \: ^{log3} ) = log \:( x)$

Using logarithm rule,

that is

$log \: a {}^{b} \: = \: b \: log \: {a} \:$

We get,

$(log3 )(log16) = log \: (x)$

This is equal to

$(log \: 3)(log \: {4}^{2} ) = log \: (x)$

Using that rule again,

$(log \: 3) \: 2 \: (log \: 4) = log \: (x)$

For other side,

Using the same process, we get,

$(log4 )(log9) = log \: (x)$

$(log \: 4)(log \: {3}^{2} ) = log \: (x)$

$log \: y \: = \: (log \: 3) \: (2)(log \: 4)$

As log (x) = log (y),

Therefore,

The given two are equal.