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: Rewrite the logarithmic equation in exponential form The given equation is: \[ \log_2 (x - 1) = 3 \] By the definition of logarithms, we can rewrite this equation in exponential form: \[ x - 1 = 2^3 \] \[ x - 1 = 8 \] Step 2: Solve for \( x \) \[ x = 8 + 1 = 9 \] Answer: Therefore, the value of \( x \) is \( 9 \). So, the correct answer is option (3).