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

Sep 26, 2016

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:

## ${\log}_{a} x = {\log}_{b} \frac{x}{\log} _ b a$

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 $\log 5$.

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

3. Press $28$ and $\log$ to display $\log 28$

4. Press $\div$ (division) button

5. Press $R M$ to recall the result stored in pt. 2.

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