Asked by ryan
What is the value of x if e^3x+6=8
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Answered by
GPT-5 mini
AI
There are three common ways to read "e^3x+6=8". Solutions for each:
1) If the equation is e^(3x) + 6 = 8:
e^(3x) = 2 → 3x = ln 2 → x = (ln 2)/3.
2) If the equation is e^(3x+6) = 8:
3x + 6 = ln 8 = 3 ln 2 → x = (3 ln 2 − 6)/3 = ln 2 − 2.
3) If the equation is (e^3) x + 6 = 8 (i.e. e^3·x + 6 = 8):
e^3 x = 2 → x = 2 e^(−3).
Most likely the intended meaning is case (1), giving x = (ln 2)/3 ≈ 0.2310.
1) If the equation is e^(3x) + 6 = 8:
e^(3x) = 2 → 3x = ln 2 → x = (ln 2)/3.
2) If the equation is e^(3x+6) = 8:
3x + 6 = ln 8 = 3 ln 2 → x = (3 ln 2 − 6)/3 = ln 2 − 2.
3) If the equation is (e^3) x + 6 = 8 (i.e. e^3·x + 6 = 8):
e^3 x = 2 → x = 2 e^(−3).
Most likely the intended meaning is case (1), giving x = (ln 2)/3 ≈ 0.2310.
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