SOLUTION: solve log(base 9)(2x+1) - log(base 3)(x-1) = 0

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Question 691408: solve log(base 9)(2x+1) - log(base 3)(x-1) = 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
+log%289%2C2x%2B1%29+-+log%283%2Cx-1%29+=+0....convert to base 10

log%282x%2B1%29%2F+log%289%29+-log%28x-1%29%2F+log%283%29=+0

log%28%282x%2B1%29%29%2F+log%28%283%5E2%29%29+-log%28%28x-1%29%29%2F+log%28%283%29%29=+0

log%28%282x%2B1%29%29%2F+2%2Alog%28%283%29%29+-log%28%28x-1%29%29%2F+log%28%283%29%29=+0

%28log%28%282x%2B1%29%29+-2%2Alog%28%28x-1%29%29%29%2F+2%2Alog%28%283%29%29=+0

=> if %28log%28%282x%2B1%29%29+-2%2Alog%28%28x-1%29%29%29=0 whole equation above is equal to zero

if %28log%28%282x%2B1%29%29+-2%2Alog%28%28x-1%29%29%29=0, than

log%28%282x%2B1%29%29+=2%2Alog%28%28x-1%29%29

log%28%282x%2B1%29%29+=log%28%28%28x-1%29%5E2%29%29

=> %282x%2B1%29+=%28x-1%29%5E2.....solve for x

2x%2B1=x%5E2-2x%2B1

x%5E2-2x-2x-1%2B1=0

x%5E2-4x=0

x%28x-4%29=0.......only if %28x-4%29=0 whole equation x%28x-4%29=0

so, if %28x-4%29=0 ...=> x=4