Question

If a, b are the solutions of the equation log base 3 (5-2x)+ log base 3 (5+2x)=2

find the value of the product ab.

Answer 1

3^2 = (5 + 2x)(5 - 2x) = 25 - 4x^2

4x^2 = 16
x^2 = 4
x = 2 or -2 are the two solutions.

The product of those two solutions is -4.

This is not a trig question. It is about logartithms and algebra.