Just A Quadratic, Right?

Algebra Level 3

Find the number of solution(s) of $x$ satisfying $\log_{4}(x - 1) = \log_{2}(x - 3)$ .

0 1 2 3

1 solution

A Former Brilliant Member
Apr 3, 2016

$\log_4{(x-1)}=\log_4{(x-3)^2}$ or $x-1=(x-3)^2$ or $x^2-7x+10=0$ or $x=5$ or $x=2$ .

But $x=5$ is the only solution because if $x=2$ then $x-3$ will be negative.