How do you simplify log_4 8?

1 Answer
May 7, 2016

Use the logarithmic properties:

log_a(b^c)=c*log_a(b)

log_a(b)=log_c(b)/log_c(a)

You can notice that c=2 fits this case since 8 can be derived as a power of 2. Answer is:

log_(4)8=1.5

Explanation:

log_(4)8

log_(2)8/log_(2)4

log_(2)2^3/log_(2)2^2

(3*log_(2)2)/(2*log_(2)2)

3/2

1.5