SOLUTION: Please help me solve x from: log<sub>4</sub>(2x) - log<sub>4</sub>(x-1) = -1 Thank you

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Question 823317: Please help me solve x from: log4(2x) - log4(x-1) = -1
Thank you
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+log%284%2C%282x%29%29-log%284%2C%28x-1%29%29+=+-1+

+log%284%2C%282x%2F%28x-1%29%29%29+=+-1+

+2x%2F%28x-1%29+=+4%5E%28-1%29+

+2x%2F%28x-1%29+=+1%2F%284%5E1%29+

+2x%2F%28x-1%29+=+1%2F4+

+2x%2A4+=+1%28x-1%29+

+8x+=+x-1+

+8x-x+=+-1+

+7x+=+-1+

+x+=+-1%2F7+

I'll let you perform the check.

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
log4(2x) - log4(x-1) = -1

Use the rule log%28B%2C%28A%29%29=log%28B%2C%28C%29%29=log%28B%2C%28A%2FC%29%29

log4%28%282x%29%2F%28x-1%29%29 = -1

Use the rule for changing a logarithm equation to an equivalent
exponential equation: log%28B%2C%28A%29%29=C is equivalent to A=B%5EC:

%28%282x%29%2F%28x-1%29%29 = 4-1

Use the rule for a negative exponent:

%28%282x%29%2F%28x-1%29%29 = 1%2F4

Cross multiply:

8x = x-1
7x = -1
 x = %28-1%29%2F7
 x = -1%2F7

Edwin