Question

How do you solve for x?: `log_3 (x-2) + log_3 (x-4) = 2`

Answer 1

I found `x=6.1623`

Explanation:

We can combine the two logs as:
`log_3[(x-2)(x-4)]=2`
Use the definition of log to get:
`(x-2)(x-4)=3^2`
`x^2-4x-2x+8=9`
`x^2-6x-1=0`
`x_(1,2)=(6+-sqrt(36+4))/2=` two solutions:
`x_1=6.1623`
`x_2=-0.1623` NO