Question

Solve for \( x \): \( \log_2 (x-1) = 3 \).

• A. \( x = 9 \)
• B. \( x = 7 \)
• C. \( x = 8 \)
• D. \( x = 6 \)

Hint:

Remember: To solve logarithmic equations, rewrite them in exponential form and then solve for the unknown variable.

Answer 1

The Correct Option is C

Step 1: Convert the logarithmic equation to exponential form Equation: \[\log_2 (x - 1) = 3\]Exponential form: \[x - 1 = 2^3\]\[x - 1 = 8\]Step 2: Isolate \( x \) \[x = 8 + 1 = 9\]Solution: The value of \( x \) is \( 9 \). Option (3) is the correct answer.