Solve log_2(3x) = 3.

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Multiple Choice

Solve log_2(3x) = 3.

Explanation:
Translating a logarithmic statement into an exponential one is the move here: if log base 2 of (3x) equals 3, then the argument 3x must be 2^3. Since 2^3 is 8, you get 3x = 8, so x = 8/3. The domain requires the argument of the log to be positive, so 3x > 0, which holds for x = 8/3. Quick check: log_2(3·(8/3)) = log_2(8) = 3, so it works. Other numbers would give different results when you evaluate the logarithm, confirming this is the correct value.

Translating a logarithmic statement into an exponential one is the move here: if log base 2 of (3x) equals 3, then the argument 3x must be 2^3. Since 2^3 is 8, you get 3x = 8, so x = 8/3. The domain requires the argument of the log to be positive, so 3x > 0, which holds for x = 8/3. Quick check: log_2(3·(8/3)) = log_2(8) = 3, so it works. Other numbers would give different results when you evaluate the logarithm, confirming this is the correct value.

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