Question

Which expression is equivalent to log2 9x^3

Answer 1

The Correct Answer Is A. log29+3log2x

Answer 2

ANSWER

$log_{2}(9 {x}^{3} ) = log_{2}(9 ) +3 log_{2}( {x} )$


EXPLANATION

We have the logarithmic expression,
$log_{2}(9 {x}^{3} )$


Recall the product rule of logarithm,




$log_{a}( MN ) = log_{a}( M) + log_{a}( N )$

We apply thus law to get,



$log_{2}(9 {x}^{3} ) = log_{2}(9 ) + log_{2}( {x}^{3} )$


Recall again that,
$log_{a}( { M}^{n} ) =n log_{a}( { M})$

We apply this law too to obtain,



$log_{2}(9 {x}^{3} ) = log_{2}(9 ) +3 log_{2}( {x} )$