Question

log(base 4) 1/8=

Answer 1

\[\text{Log}_4\left(\frac{1}{8}\right)\]

Answer 2

-1.5

Answer 3

I am not sure if there is a way to solve by hands

Answer 4

Change of base law.

Answer 5

@imran.

Answer 6

\[\frac{\text{Log}_{10 }\frac{1}{8}}{\text{Log}_{10}4}\]
Yeah , but you can't solve by hand

Answer 7

Yeah/

Answer 8

Ye of little faith..
\[Let\ k = log_4(\frac{1}{8})\]
\[log_4(\frac{1}{8}) = k \iff 4^k = \frac{1}{8}\]\[\implies 4^k = 2^{-3}\]\[\implies (2^2)^k = 2^{-3}\]\[\implies 2^{2k} = 2^{-3}\]\[\implies 2k = -3\]\[\implies k = -\frac{3}{2}\]\[\implies log_4(\frac{1}{8}) = -\frac{3}{2} = -1.5\]