SOLUTION: Solve the logarithmic equation: 2log(6x)-log(9)=log(36)

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Question 945219: Solve the logarithmic equation:
2log(6x)-log(9)=log(36)
Found 2 solutions by ankor@dixie-net.com, Alan3354:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the logarithmic equation:
2log(6x) - log(9) = log(36)
the exponent equiv of logs
log%28%286x%29%5E2%29+-+log%28%289%29%29+=+log%28%2836%29%29
log%28%2836x%5E2%29%29+-+log%28%289%29%29+=+log%28%2836%29%29
Subtracting of logs means divide. Cancel the 9 into 36
log%28%28%2836x%5E2%29%2F9%29%29+=+log%28%2836%29%29 = log%28%284x%5E2%29%29+=+log%28%2836%29%29
if the log of one number equals the log of an other number. The values are equal
4x%5E2+=+36
divide both sides by 4
x%5E2+=+9
x+=+sqrt%289%29
x = 3


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2log(6x)-log(9)=log(36)
2log(6x) = log(9) + log(36)
Adding logs --> multiplication
2log(6x) = log(9*36) = log(324)
log(6x) + log(6x) = log(324)
log((6x)^2) = log(324)
log(36x^2) = log(324)
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If the logs are equal, then
36x^2 = 324
x^2 = 9
x = 3
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x = -3 is rejected, --> log of a negative number