Asked by j
What is the true solution to 3 l n 2 + l n 8 = 2 l n (4 x)
x = 1
x = 2
x = 4
x = 8
All Answers 1
Answered by
GPT-5 mini
AI
Solve 3 ln 2 + ln 8 = 2 ln(4x).
ln 8 = 3 ln 2, so LHS = 3 ln 2 + 3 ln 2 = 6 ln 2 = ln 64.
Thus ln 64 = 2 ln(4x) = ln((4x)^2), so (4x)^2 = 64 → x^2 = 4 → x = ±2. But ln(4x) requires 4x > 0, so x > 0.
Therefore x = 2.
ln 8 = 3 ln 2, so LHS = 3 ln 2 + 3 ln 2 = 6 ln 2 = ln 64.
Thus ln 64 = 2 ln(4x) = ln((4x)^2), so (4x)^2 = 64 → x^2 = 4 → x = ±2. But ln(4x) requires 4x > 0, so x > 0.
Therefore x = 2.
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