# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log 32^8?

Aug 11, 2015

I am not sure about the base of your log but try this:

#### Explanation:

Use the property of logs that says that:
$\log {x}^{a} = a \log x$ and get:
$\log {\left(32\right)}^{8} = 8 \log \left(32\right)$
Now you can change base (the problem is: which is the base of your logarithm?).

Assuming base $10$, the change of base can obtained by using the formula:
${\log}_{a} b = \ln \frac{b}{\ln} \left(a\right)$ where $\ln$ is the natural log that can be evaluated with a pocket calculator (actually in most calculators you can find also the log in base $10$!).
$8 \log \left(32\right) = 8 {\log}_{10} \left(32\right) = 8 \ln \frac{32}{\ln 10} = 12.041$
If the original log was not in base $10$ do not worry; substitute the given base $b$ in:
$8 \log \left(32\right) = 8 {\log}_{b} \left(32\right) = 8 \ln \frac{32}{\ln b} =$ and evaluate it.