SOLUTION: Solve. Round to the nearest 100ths if necessary. log5(x+8)=2log5(6)

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Question 1210718: Solve. Round to the nearest 100ths if necessary.
log5(x+8)=2log5(6)
Answer by ikleyn(54060) About Me  (Show Source):
You can put this solution on YOUR website!
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Solve. Round to the nearest 100ths if necessary.
log5(x+8)=2log5(6)
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I interpret the given equation this way

    log%285%2C%28x%2B8%29%29 = 2%2Alog%285%2C%286%29%29.


Using properties of logarithms, rewrite it 

    log%285%2C%28x%2B8%29%29 = log%285%2C%286%5E2%29%29,

    log%285%2C%28x%2B8%29%29 = log%285%2C%2836%29%29.


Since the logarithms are equal and the bases are the same, the arguments are equal

    x + 8 = 36.


It implies

    x = 36 - 8,

    x = 28.                ANSWER


To check, substitute x=6 into the equation.

You will get log%285%2C%2836%29%29 on the left side, which equals the right side 2%2Alog%285%2C%286%29%29.

So, the equation is solved correctly.