Question

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

Answer 1

`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`