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

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

Answer by hkwu(60) (Show Source): You can put this solution on YOUR website!
No, equations of the form

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:

The equation has no solution as it would imply that

if it was true, which is obviously not the case.
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