# How do you solve log_5(3x^2 - 1) = log_5 2x?

May 19, 2016

x = 1.

#### Explanation:

Logarithm is a single-valued function.

So, $3 {x}^{2} - 1 = 2 x$. Solving this quadratic equation

$3 {x}^{2} - 2 x - 1 = 0 , x = 1. - \frac{1}{2}$

Negative root is inadmissible for #log_5(2x).

So, x = 1.