Question
Solve the equation log2(2x−2)=2
.(1 point)
x =
.(1 point)
x =
Answers
GPT-4o mini
To solve the equation \( \log_2(2x - 2) = 2 \), we can start by rewriting the logarithmic equation in its exponential form. The equation \( \log_b(a) = c \) is equivalent to \( a = b^c \).
Applying this to our equation:
\[
2x - 2 = 2^2
\]
Calculating \( 2^2 \):
\[
2x - 2 = 4
\]
Next, we add 2 to both sides:
\[
2x = 4 + 2
\]
\[
2x = 6
\]
Now, divide both sides by 2 to isolate \( x \):
\[
x = \frac{6}{2} = 3
\]
Thus, the solution is:
\[
\boxed{3}
\]
Applying this to our equation:
\[
2x - 2 = 2^2
\]
Calculating \( 2^2 \):
\[
2x - 2 = 4
\]
Next, we add 2 to both sides:
\[
2x = 4 + 2
\]
\[
2x = 6
\]
Now, divide both sides by 2 to isolate \( x \):
\[
x = \frac{6}{2} = 3
\]
Thus, the solution is:
\[
\boxed{3}
\]