Step by step
The question
Question: solve log₄(x − 1) = 2.
log4(x − 1) = 2
1 Write it as a power
A log is a power.
log₄(x − 1) = 2 means: 4 to the power 2 is x − 1.
log4 c = k means 4k = c
So x − 1 is 4².
x − 1 = 42
2 Work out the power
4 times 4 is 16.
4 × 4 = 16
Now we have x − 1 = 16.
x − 1 = 16
3 Remove the − 1
We want x by itself.
The − 1 is in the way.
To remove − 1, we add 1.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
x − 1 + 1 = 16 + 1
− 1 and + 1 make zero.
Cross them out.
16 + 1 = 17.
16 + 1 = 17
So x = 17!
x = 17
4 Check
Let's check: put 17 in place of x.
Check: log4(17 − 1) = log4 16
log₄ 16 is 2, because 4² is 16.
So x = 17 is right!
log4 16 = 2, because 42 = 16
Let's look back.
First: write it as a power.
Then: work out the power.
Then: remove the − 1.
Last: check.
Answer
x = 17