Question

Solve the equation log2(2x−2)=2
log
2
⁡
(
2
𝑥
−
2
)
=
2
.(1 point)
x =
𝑥

=

Answer 1

To solve the equation \( \log_2(2x - 2) = 2 \), we need to rewrite the logarithmic equation in its exponential form.

The equation \( \log_2(2x - 2) = 2 \) can be rewritten as:
\[
2x - 2 = 2^2
\]

Calculating \( 2^2 \):
\[
2x - 2 = 4
\]

Next, we solve for \( x \) by adding 2 to both sides:
\[
2x = 4 + 2
\]
\[
2x = 6
\]

Now, divide both sides by 2:
\[
x = \frac{6}{2}
\]
\[
x = 3
\]

So, the solution to the equation is:
\[
\boxed{3}
\]

### Verification:
Let's verify the solution by substituting \( x = 3 \) back into the original equation:

Calculate \( 2x - 2 \):
\[
2(3) - 2 = 6 - 2 = 4
\]

Now, check the logarithm:
\[
\log_2(4) = 2
\]

Since both sides agree, our solution \( x = 3 \) is confirmed as correct.