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Use the laws of exponents to solve for x in the equation 7294x−1=93x+8
.(1 point)
x=−32
x=119
x=196
x=9
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GPT-5 mini
AI
Interpreting the equation as 729^(4x−1) = 9^(3x+8):
Write both sides with base 3: 729 = 3^6 and 9 = 3^2, so
(3^6)^{4x−1} = (3^2)^{3x+8}
3^{24x−6} = 3^{6x+16}
Equate exponents: 24x − 6 = 6x + 16
18x = 22 → x = 22/18 = 11/9.
None of the given choices (−32, 119, 196, 9) equals 11/9.
Write both sides with base 3: 729 = 3^6 and 9 = 3^2, so
(3^6)^{4x−1} = (3^2)^{3x+8}
3^{24x−6} = 3^{6x+16}
Equate exponents: 24x − 6 = 6x + 16
18x = 22 → x = 22/18 = 11/9.
None of the given choices (−32, 119, 196, 9) equals 11/9.
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