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

1 Answer
Mar 2, 2018

2log_2 7+14

Explanation:

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