Question 687487: Solve 3^x-1=7
Write 6log4x+log4y as a single logarithm
Solve.
3^2x-1 x 81^2/4
__________________ = 9^5x
27^1-x Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Solve 3^x-1=7
3^(x-1) = 7
(x-1)*log(3) = log(7)
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x*log(3) = log(3)+log(7)
x = log(21)/log(3)
x = 2.77
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Write 6log4x+log4y as a single logarithm
6*log4(x) + log4(y)
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= log4(x^6)+log4(y)
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= log4[x^6*y]
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Solve.
3^2x-1 x 81^2/4
__________________ = 9^5x
27^1-x
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[3^(2x-1)*(3^4)^(2/4)]/(3^3)^(1-x) = (3^2)^5x
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[(3)^(2x-1)*(3^2)]/3^(3-3x) = 3^10x
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[3^(2x+1)/3^(3-3x)] = 3^10x
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[3^(5x-2)] = 3^10x
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5x-2 = 10x
5x = -2
x = -2/5
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Cheers,
Stan H.
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