log_3(3^(x-8))=2-x solve the equation?

2 Answers
Jun 7, 2018

x = 5

Explanation:

Given: log_3(3^(x-8))=2-x

Using the property log_b(b^u) = u we change the left side:

x-8=2-x

Solve for x:

2x = 10

x = 5

Jun 7, 2018

x=5

Explanation:

On the left side, since we have the same base, we can rewrite our expression as the following:

cancel(log_3)(cancel3^(x-8))=2-x

=>x-8=2-x

Now this is just a simple algebra equation. Let's add x to both sides to get

2x-8=2

Adding 8 to both sides, we get

2x=10

Lastly, we divide both sides by 2 to get

x=5

Hope this helps!