Question

Solve the following log without using a calculator.
10^x^2-4 = 1

Answer 1

\[10^{x^2-4}=1\]

Answer 2

So far using the prop of logs, I have:
\[\log_{10}10^{x^2-4}=\log_{10}1 \]

Answer 3

canceling that log10 on the left gives me: \[x^2-4\] but I'm not sure what I do for the right side.

Answer 4

\[
10^{0}=1
\]

Answer 5

You can use x^2 - 4 = 0
Then solve x

Answer 6

In Mathematics you should NEVER Canel logs.

Answer 7

@wio Oh right, I forgot about that.

Answer 8

From there I just move the 4 over to the left side and square both sides to get the following:
\[x=\pm \sqrt{2}\]
right?

Answer 9

how did you get \(\sqrt 2\)?

Answer 10

oh sorry it would just be -2 and +2
Could I also factor it to get:
\[(x+2)(x-2)=0\]
\[x=\pm2\]