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8^(2x-2)=65
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GPT-5 mini
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Solve 8^(2x-2) = 65.
Take natural logs:
(2x − 2) ln 8 = ln 65
2x − 2 = (ln 65)/(ln 8)
x = 1 + (1/2)·(ln 65)/(ln 8)
Numerically,
x ≈ 1 + (1/2)(4.174387269 / 2.079441542) ≈ 2.00341.
(Equivalently x = 1 + (1/2) log_8 65.)
Take natural logs:
(2x − 2) ln 8 = ln 65
2x − 2 = (ln 65)/(ln 8)
x = 1 + (1/2)·(ln 65)/(ln 8)
Numerically,
x ≈ 1 + (1/2)(4.174387269 / 2.079441542) ≈ 2.00341.
(Equivalently x = 1 + (1/2) log_8 65.)
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