Step by step
The question
Question: solve log₃(2x + 1) = 2.
1 Write it as a power
A log is a power.
log₃(2x + 1) = 2 means: 3 to the power 2 is 2x + 1.
So 2x + 1 is 3².
2 Work out the power
3 times 3 is 9.
Now we have 2x + 1 = 9.
We want x by itself.
Two things are stuck to x: times 2 and + 1.
The + 1 is on the outside, so it comes off first.
Then the times 2.
3 Remove the + 1
To remove + 1, we take away 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.
+ 1 and − 1 make zero.
Cross them out.
9 − 1 = 8.
Now we have 2x = 8.
4 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
8 divided by 2 is 4.
So x = 4!
5 Check
Let's check: put 4 in place of x.
log₃ 9 is 2, because 3² is 9.
So x = 4 is right!
Let's look back.
First: write it as a power.
Then: work out the power.
Then: remove the + 1.
Then: remove the 2.
Last: check.