How do you simplify $log_2 (4^2*3^4)$ ?

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Answer 1 · 2017-01-12T20:25:41

$4+4log_2 3$

You would use some properties of logarithms:

1) $log(a*b)=loga+logb$

2) $loga^b=bloga$

then

$log_2(4^2*3^4)=log_2(4^2)+log_2(3^4)$ $->$ property 1)

$=2log_2 4+4log_2 3$ $->$ property 2)

Since $log_2 4=2$ ,

the expression becomes

$2*2+4log_2 3=4+4log_2 3$

How do you simplify log_2 (4^2*3^4)log_2 (4^2*3^4)?