Solve: log₃(x + 1) = 4

Question

Accepted Answer

x = 80. The correct answer is x = 80. Converting from logarithmic to exponential form: log₃(x + 1) = 4 means 3⁴ = x + 1, so 81 = x + 1, giving x = 80. Verify: log₃(80 + 1) = log₃(81) = log₃(3⁴) = 4 ✓.

The value x = 81 forgets to subtract 1 from both sides after converting to exponential form. Since x + 1 = 81, we need x = 80, not 81. The value x = 12 may come from multiplying 3 × 4 = 12, confusing logarithmic relationships with multiplication. The value x = 11 may arise from computing 3 + 4 + 4 = 11 or some other incorrect arithmetic.

Solving logarithmic equations by converting to exponential form is a fundamental skill for the CLEP exam. The relationship log_b(x) = y is equivalent to b^y = x. Students should be comfortable moving between these forms and remembering to solve for the original variable after converting. Always verify the solution makes the argument of the logarithm positive.

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