A student writes ln(x2-1)=ln(x-1)+ln(x+1) for every real x for which the left side exists. Determine

Question

A student writes ln(x2-1)=ln(x-1)+ln(x+1) for every real x for which the left side exists. Determine the exact set of x for which the equality is valid, and give a counterexample to the student’s claim.

Accepted Answer

$x>1$; counterexample $x=-2$.

When expanding changes the domain

When expanding changes the domain

Solution:

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