How do you simplify $log_2 (7^2 * 4^7)$ ?

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Answer 1 · 2018-03-02T19:22:16

$2log_2 7+14$

You have to use the properties of logs.
Addition property: $log_b (xy)=log_b x+log_b y$
Power property: $log_b (x^y)=ylog_b x$

By the addition property, $log_2 (7^2times4^7)=log_2 (7^2)+log_2 (4^7)$

By the power property, $log_2 *(7^2)=2log_2 7$ and $log_2 (4^7)=7log_2 4$

So $log_2 (7^2times4^7)=2log_2 7+7log_2 4$

$log_2 4 = 2$ so this evaluates as:

$log_2 (7^2times4^7)=2log_2 7+7(2)=2log_2 7+14$

How do you simplify log_2 (7^2 * 4^7)log_2 (7^2 * 4^7)?