Question

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

Answer 1

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=ln1/ln2=0`

using our calculator.

Answer 2

`log_10 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 y / log_10 x`

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

As for the calculator part, calculator `log(x)` is always equal to `log_10(x)`, so instead of worrying about your bases of ten, just plug in:

`log(1)/log(2)`

You should get

`log(1)/log(2)=0`