Question

How do you calculate `log_5 (-28)` with a calculator?

Answer 1

See explanation.

Explanation:

The given logarythm cannot be calculated because `log` is only defined for positive values, but there is a procedure of calculating any legal logatrythm using a calculator.

To do this we have to use the Change of Base Formula, which is:

`log_ax=log_bx/log_ba`

This formula lets us change the logarythm with non standard base to a quotient of logarythms of any other base.

Calculators don't have logarythm of base `5`, but they usually have either natural logarythm `ln` or base 10 logarythm `log`. I will explain the procedure using base `10`.

The procedure is:

1. Press `5` and `log` to calculate `log5`.

2. Press `M` to put the result in memory.

3. Press `28` and `log` to display `log28`

4. Press `-:` (division) button

5. Press `RM` to recall the result stored in pt. 2.

6. Press `=` to calculate the final result.