Calculate log_2(1/8)

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

Step by step

Question: work out log₂(1/8).

log₂(18)

A log is a power.

log₂(1/8) asks: 2 to what power is 1/8?

a log is a power

2 to the power what is 1/8?

2^? = 18

8 is 2³.

A minus power means 1 over.

So 1/2³ is 2⁻³.

2 × 2 × 2 = 8

12³ = 2⁻³

So the power is −3.

2⁻³ = 18

So log₂(1/8) = −3.

log₂(18) = −3

Let's look back.

First: what the log asks.

Last: find the power.

Answer

log₂(18) = −3

Try this one yourself, then check:

log₄(116)

Show the answer

log₄(116) = −2