Asked by Ryu
Solve. Write your answer as an integer or a fraction in simplest form.
94x–4=
1
81
x–4
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the equation as 9^{4x-4} = (1/81)^{x-4}.
Write both sides with base 3: 9 = 3^2 and 1/81 = 3^{-4}, so
(3^2)^{4x-4} = (3^{-4})^{x-4}
3^{8x-8} = 3^{-4x+16}
Equate exponents: 8x-8 = -4x+16 → 12x = 24 → x = 2.
Answer: 2
Write both sides with base 3: 9 = 3^2 and 1/81 = 3^{-4}, so
(3^2)^{4x-4} = (3^{-4})^{x-4}
3^{8x-8} = 3^{-4x+16}
Equate exponents: 8x-8 = -4x+16 → 12x = 24 → x = 2.
Answer: 2
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