Evaluate:
log4 (1/8)
how can i solve without a calculator. i know this answer is -1.5
= log(1/8)
log 4
I would not use a change of base rule here. What you want is $\displaystyle \frac{1}{8}$ in terms of 4's, i.e., $\displaystyle \frac{1}{2}\cdot \frac{1}{4} = \left(\frac{1}{4}\right)^{0.5}\cdot \frac{1}{4}$. Now you can use your log rules to calculate the actual value.
Hello, danielh9103!
Evaluate: .$\displaystyle \log_4\!\left(\frac{1}{8}\right)$
Let: .$\displaystyle \log_4\!\left(\frac{1}{8}\right) \:=\:P$
Then: .$\displaystyle 4^P \:=\:\dfrac{1}{8} \quad\Rightarrow\quad (2^2)^P \:=\:\dfrac{1}{2^3} \quad\Rightarrow\quad 2^{2P} \:=\:2^{-3}$
Hence: .$\displaystyle 2P \:=\:-3 \quad\Rightarrow\quad P \:=\:-\frac{3}{2}$
Therefore: .$\displaystyle \log_4(\frac{1}{8}) \;=\;-\frac{3}{2}$