# How do you show that this statement is true #log_16 2*log_2 16=1#?

##### 1 Answer

Nov 18, 2016

#### Answer:

see explanation.

#### Explanation:

Using the

#color(blue)"laws of logarithms"#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(log_b x=nhArrx=b^n)color(white)(2/2)|)))#

#rArrlog_16 2=nrArr2=16^nrArrn=1/4#

#"and " log_2 16=nrArr16=2^nrArrn=4#

#rArrlog_16 2xxlog_2 16=1/4xx4=1" hence True"#