Question

Simplify to the extent possible (logx16)(log2x)

Answer 1

Answer:

${ \tt{ = ( log_{x}16)( log_{2}x) }}$

Change base x to base 2:

${ \tt{ = (\frac{ log_{2}16}{ log_{2}x } )( log_{2}x)}} \\ \\ { \tt{ = log_{2}(16) }} \\ = { \tt{ log_{2}(2) }} {}^{4} \\ = { \tt{4 log_{2}(2) }} \\ = { \tt{4}}$