SOLUTION: log[5](x-2)+log[5](2x-9)=2

Question 205989: log[5](x-2)+log[5](2x-9)=2
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
log(5){x-2} +log(5){2x-9} = 2
.
log a + log b = log a*b
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log(5) { (x-2)(2x-9)} = 2
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log(a) b = log b / log a
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log{ (x-2)(2x-9)} / log(5) = 2
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log{ 2x^2 -9x -4x +18} = 2 log 5 = 1.3979
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Raise each side as power of 10,,,,10^(log a) =a
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{ 2x^2 -13x +18} = 10^1.3979 = 25
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2x^2 -13x -7 =0,,,,,,,,factor
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(2x+1)(x-7) =0
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x = 7,,,, - 1/2 ( not realistic)
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check,,(x=7),,,,,,log(5){5} +log(5){5} = 2
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log 25 / log 5 = 2
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log 25 =2 log 5 = 1.3979,,,,,,ok
.

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