SOLUTION: 0= log base 5 (x-2) - log base 5 (2x)

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Question 975452: 0= log base 5 (x-2) - log base 5 (2x)
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20854) About Me  (Show Source):
You can put this solution on YOUR website!

0=+log%285%2C+%28x-2%29%29+-+log%285+%2C%282x%29%29
0=+log%285%2C+%28x-2%29%2F2x%29.......since log%285%2C1%29=0, we have
log%285%2C1%29=+log%285%2C+%28x-2%29%2F2x%29....since log and bases same, we have
1=+%28x-2%29%2F2x......solve for x
1%2A2x=+%28x-2%29
2x=+x-2
2x-x=-2
x=-2

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
0= log base 5 (x-2) - log base 5 (2x)

0+=+log+%285%2C+%28x+-+2%29%29+-+log+%285%2C+%282x%29%29
Smaller variable-expression, x - 2 MUST be > 0. We then get: x - 2 > 0___x MUST be > 2. The problem then becomes:
0+=+log+%285%2C+%28x+-+2%29%29+-+log+%285%2C+%282x%29%29, with x > 2.

When solved, we get x = - 2. However, because this x-value is NOT > 2, there are NO SOLUTIONS to this LOGARITHMIC equation.

So, IGNORE the other person's answer that x = - 2.