# How do you solve #ln ( x - 1) + ln x - ln ( x^2 + x - 2 ) = 0#?

##### 1 Answer

Dec 17, 2015

The equation has no solution.

#### Explanation:

Know the following rule:

Basically, if logarithms with the same base are being added, the terms on the interior can be multiplied. If they're being subtracted, the terms are divided.

Thus, the equation can be simplified as

Factor the denominator.

Simplify.

Rewrite, recalling that

This equation has no solutions.

This can be confirmed by checking a graph.

graph{ln(x-1)+ln(x)-ln(x^2+x-2) [-1.29, 18.71, -3.8, 6.2]}

The graph approaches the