Question

How do you solve `log_4(x+1) - log_4(x-2) = 3`?

Answer 1

I found: `x=2.04762`

Explanation:

You can use the property of logs that tells us:
`logx-logy=log(x/y)`
to get:
`log_4((x+1)/(x-2))=3`
Now we use the definition of log to change it into an exponential:
`(x+1)/(x-2)=4^3`
`(x+1)/(x-2)=64`
`(x+1)=64(x-2)`
`x+1=64x-128`
`63x=129`
`x=129/63=2.04762`