How do you solve log_2(9x+5)=2+log_2(x^2-1)?

1 Answer
Oct 16, 2016

x=-3/4 or3

Explanation:

We need to write 2 in the form of log_2?
2^2=4 so log_2 4=2

Rewrite the equation as
log_2(9x+5)=log_2 4+log_2(x^2-1)
Or using the addition rule of logs
log_2(9x+5)=log_2 4(x^2-1)
Therefore
9x+5=4(x^2-1)
Rearrange
9x+5=4x^2-4
4x^2-9x-9=0
Factorise
(4x+3)(x-3)=0
Thus x=-3/4 or3