# Thread: Solving Without a Calculator?

1. ## Solving Without a Calculator?

Evaluate:

log4 (1/8)

how can i solve without a calculator. i know this answer is -1.5

= log(1/8)
log 4

2. I would not use a change of base rule here. What you want is $\frac{1}{8}$ in terms of 4's, i.e., $\frac{1}{2}\cdot \frac{1}{4} = \left(\frac{1}{4}\right)^{0.5}\cdot \frac{1}{4}$. Now you can use your log rules to calculate the actual value.

3. Hello, danielh9103!

Evaluate: . $\log_4\!\left(\frac{1}{8}\right)$

Let: . $\log_4\!\left(\frac{1}{8}\right) \:=\:P$

Then: . $4^P \:=\:\dfrac{1}{8} \quad\Rightarrow\quad (2^2)^P \:=\:\dfrac{1}{2^3} \quad\Rightarrow\quad 2^{2P} \:=\:2^{-3}$

Hence: . $2P \:=\:-3 \quad\Rightarrow\quad P \:=\:-\frac{3}{2}$

Therefore: . $\log_4(\frac{1}{8}) \;=\;-\frac{3}{2}$

4. log(1/8)=log(1/2^3)=log(2^(-3))=-3log2=-3/2