SOLUTION: Find the exact value solution log (5x) + log (x-1) = 2

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Question 759176: Find the exact value solution
log (5x) + log (x-1) = 2
Found 2 solutions by sachi, MathTherapy:
Answer by sachi(548) (Show Source):
You can put this solution on YOUR website!
log (5x) + log (x-1) = 2
or log[5x(x-1)]=2
or 5x(x-1)=AntiLog(2) = 102=100
or x(x-1)=100/5=20
or x^2-x-20=0
or x^2-5x+4x-20=0
or x(x-5)+4(x-5)=0
or (x-5)(x+4)=0
or x=5 or -4

Answer by MathTherapy(10806) (Show Source):
You can put this solution on YOUR website!

Find the exact value solution log (5x) + log (x-1) = 2 ************************************* x = 5 or - 4, as stated by the other person, is partly WRONG! log (5x) + log (x - 1) = 2 Looking at the logarithmic equation, the smaller log argument, x - 1 MUST be > 0. So, x - 1 > 0, and therefore, x > 1. We then have: log (5x) + log (x - 1) = 2, with x > 1 So, x = 5 is the ONLY solution, as x = - 4 is EXTRANEOUS.