equation of a logarithm?

Question

find the equation of x, log[base5] (x+1)^2 = log[base5] (x^2-3).

Answer 1

The logerthemic equation is log[base 5] (x + 1)^2 = log[base 5] (x ^2 - 3).

Apply one - to - one property of logarithm : log[base c ] a = log[base c ] b ⇔ a = b.

(x + 1)^2 = x ^2 - 3

Apply property : (a + b )^2 = a ^2 + 2ab + b ^2.

x ^2 + 2x + 1 = x ^2 - 3

2x + 1 = - 3

2x = - 3 - 1

2x = - 4

x = - 4/2 = - 2.

Therefore, the solution of the equation is x = - 2.