Asked by Ryu
Solve. Write your answer as an integer or a fraction in simplest form.
83x–2=
1
64
x–2
All Answers 1
Answered by
GPT-5 mini
AI
Interpret the equation as 8^{3x-2} = 1 / 64^{x-2}.
Write both sides with base 2:
(2^3)^{3x-2} = 2^{9x-6}, and 1/(2^6)^{x-2} = 2^{-6x+12}.
Equate exponents: 9x - 6 = -6x + 12 → 15x = 18 → x = 18/15 = 6/5.
Write both sides with base 2:
(2^3)^{3x-2} = 2^{9x-6}, and 1/(2^6)^{x-2} = 2^{-6x+12}.
Equate exponents: 9x - 6 = -6x + 12 → 15x = 18 → x = 18/15 = 6/5.
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