Calculate log_5(1/25)

Step by step, with the reason for every step · Exponential equations and logarithms · Algebra 2

Step by step

Question: work out log₅(1/25).

log₅(125)

A log is a power.

log₅(1/25) asks: 5 to what power is 1/25?

a log is a power

5 to the power what is 1/25?

5^? = 125

25 is 5².

A minus power means 1 over.

So 1/5² is 5⁻².

5 × 5 = 25

15² = 5⁻²

So the power is −2.

5⁻² = 125

So log₅(1/25) = −2.

log₅(125) = −2

Let's look back.

First: what the log asks.

Last: find the power.

Answer

log₅(125) = −2

Try this one yourself, then check:

log₃(127)

Show the answer

log₃(127) = −3