SOLUTION: Is it possible for a logarithmic equation to have no solution? If so, when would this occur?

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Question 963527: Is it possible for a logarithmic equation to have no solution? If so, when would this occur?

Answer by hkwu(60) About Me  (Show Source):
You can put this solution on YOUR website!
No, equations of the form
ln%28x%29=y
always have a solution as long as x is a valid input (i.e. x > 0). This is because logarithms have a range that extends from negative to positive infinity.
But consider this:
ln%28x%2B1%29-ln%28x%2B5%29=0
The equation has no solution as it would imply that
ln%28x%2B1%29=ln%28x%2B5%29
if it was true, which is obviously not the case.
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