Question

Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3
x = negative 1
x = 1
x = negative 1 and x = 1
x = 0, x = negative 1, and x = 1

Answer 1

Solve 3·log2(2x) = 3. Divide both sides by 3: log2(2x) = 1.
Convert to exponential form: 2x = 2^1 = 2, so x = 1.

Check domain: log2(2x) requires 2x > 0 ⇒ x > 0, so x = 1 is valid.

Answer: x = 1.