SOLUTION: log(2x-1) = log(x+3) + log3

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Question 152883: log(2x-1) = log(x+3) + log3
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
log%2810%2C%282x-1%29%29+=+log%2810%2C%28x%2B3%29%29+%2B+log%2810%2C%283%29%29 Start with the given equation.


log%2810%2C%282x-1%29%29+=+log%2810%2C%283%28x%2B3%29%29%29 Combine the logs using the identity log%28b%2C%28A%29%29%2Blog%28b%2C%28B%29%29=log%28b%2C%28A%2AB%29%29


2x-1=3%28x%2B3%29 Set the inner arguments equal to one another.


2x-1=3x%2B9 Distribute.


2x=3x%2B9%2B1 Add 1 to both sides.


2x-3x=9%2B1 Subtract 3x from both sides.


-x=9%2B1 Combine like terms on the left side.


-x=10 Combine like terms on the right side.


x=%2810%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-10 Reduce.


So the possible answer is x=-10; however, we must check it.

log%2810%2C%282x-1%29%29+=+log%2810%2C%28x%2B3%29%29+%2B+log%2810%2C%283%29%29 Start with the given equation.


log%2810%2C%282%28-10%29-1%29%29+=+log%2810%2C%28-10%2B3%29%29+%2B+log%2810%2C%283%29%29 Plug in x=-10


log%2810%2C%28-13%29%29+=+log%2810%2C%28-7%29%29+%2B+log%2810%2C%283%29%29 Simplify. Since you cannot take the log of negative number, this means that x=-10 is not a solution.

So there are no solutions.