Question

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

Answer 1

`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`