# How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_2 1?

Apr 30, 2018

I tried this:

#### Explanation:

Actually you do not even need to change base as:

${\log}_{2} 1 = 0$

because: ${2}^{0} = 1$

Anyway, we can change into natural logs and write:

${\log}_{2} 1 = \ln \frac{1}{\ln} 2 = 0$

using our calculator.

Apr 30, 2018

${\log}_{10} \frac{1}{\log} _ 10 2 = 0$

#### Explanation:

It's probably easier to study the pattern I'm putting out below than it would be to sort through my math explanation.

Change of base will always look like this:

${\log}_{x} y = {\log}_{10} \frac{y}{\log} _ 10 x$

When I learned trig earlier this year, I just memorized that formula.

As for the calculator part, calculator $\log \left(x\right)$ is always equal to ${\log}_{10} \left(x\right)$, so instead of worrying about your bases of ten, just plug in:

$\log \frac{1}{\log} \left(2\right)$

You should get

$\log \frac{1}{\log} \left(2\right) = 0$