SOLUTION: Please give step by step instructions on solving this problem... {{{3^x = 8^(x-8)}}}

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Question 462600: Please give step by step instructions on solving this problem...
3%5Ex+=+8%5E%28x-8%29
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Please give step by step instructions on solving this problem...
3%5Ex+=+8%5E%28x-8%29
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There are several ways to solve this problem Here is a method that I like. Warning: this problem has LOTS of algebra twists and turns!
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Remember that the logarithm function is the inverse of the exponential function. This means that I can rewrite any exponential equation as a logarithmic equation.
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We are given
3%5Ex+=+8%5E%28x-8%29
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Since these to expressions are equivalent, their natural logarithms are equivalent. So,
ln%283%5Ex%29=ln%288%5E%28x-8%29%29
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Using the power property for the logarithms, we have

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Now we expand the right side of the equation.
ln%283%29%2Fln%288%29=x%2Fx-8%2Fx=1-8%2Fx
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Solve for x.
ln%283%29%2Fln%288%29-1=-8%2Fx
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ln%283%29%2Fln%288%29-ln%288%29%2Fln%288%29=-8%2Fx
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ln%283%29-ln%288%29%2Fln%288%29=-8%2Fx
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%28ln%283%29-ln%288%29%29%2Fln%288%29=-8%2Fx
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Apply the division property for subtracting logarithms.
ln%283%2F8%29%2Fln%288%29=-8%2Fx
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x=%28-8%2Aln%288%29%29%2F%28ln%283%2F8%29%29
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hope this helps!
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Ms.Figgy
math.in.the.vortex