SOLUTION: Solve: 2 * Log base 4(x) + 3 * log base 8(x) = 10

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Question 332015: Solve: 2 * Log base 4(x) + 3 * log base 8(x) = 10
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
2+%2A+log%284%2Cx%29+%2B+3+%2A+log%288%2Cx%29+=+10
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need to put both logs in same base, choose one base does not matter
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log%288%2Cx%29=log%284%2Cx%29%2Flog%284%2C8%29
also log%284%2C8%29=log%282%2C8%29%2Flog%282%2C4%29=log%282%2C2%29%5E3%2Flog%282%2C2%29%5E2=3%2F2
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so...
log%288%2Cx%29=log%284%2Cx%29%2F%283%2F2%29=2%2F3%2Alog%284%2Cx%29
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subtituting

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log%284%2Cx%29=10%2F4=5%2F2
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4%5E%28log%284%2Cx%29%29=4%5E%285%2F2%29
remember that a%5E%28log%28a%2Cx%29%29=x
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x=4%5E%285%2F2%29=+%282%5E%282%29%29%5E%285%2F2%29=2%5E5+=32