Solve 3^x = 81

Step by step

The question

Question: solve 3 to the power x = 81.

x is up in the power.

1 Write 81 as a power of 3

81 is 3 times itself, 4 times.

So 81 is 3⁴.

Now both sides are 3 to a power.

2 The powers are equal

Both sides are 3 to a power.

Same base, and they are equal.

So the powers must be equal too.

So x = 4!

3 Check

Let's check: put 4 in place of x.

We get 81, the same as the right side.

So x = 4 is right!

Let's look back.

First: write 81 as a power of 3.

Then: the powers are equal.

Last: check.