Question

explain why there is no solution to the equation sin^(-1) x = log(x-1)

Answer 1

because sin^(-1)(x) is defined only at the interval (-1.1) and for any x of that interval log(x-1) is not defined, so there cant be interception

Answer 2

Take sine of both sides, you get x = sin(log(x-1)), where x > 1. But sin of anything must be less than or equal to 1, so there are no solutions.