Solve log_2(x) = 5

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

Step by step

Question: solve log₂ x = 5.

log₂ x = 5

A log is a power.

log₂ x = 5 means: 2 to the power 5 is x.

log₂ c = k means 2^k = c

So x is 2⁵.

x = 2⁵

2 times 2 times 2 times 2 times 2 is 32.

2 × 2 × 2 × 2 × 2 = 32

So x = 32.

x = 32

Let's check: put 32 in place of x.

Check: log₂ 32

log₂ 32 is 5, because 2⁵ is 32.

So x = 32 is right!

log₂ 32 = 5, because 2⁵ = 32

Let's look back.

First: write it as a power.

Then: work out the power.

Last: check.

Answer

x = 32

Try this one yourself, then check:

log₂ x = 4

Show the answer

x = 16