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

1 Answer
Mar 2, 2018

Answer:

#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#