Question

How do you solve `log_6 (x-4) ^2=2`?

Answer 1

`x_"1"=4+6^sqrt2`
`x_"2"=4+1/(6^sqrt2)`

Explanation:

`log_"6"(x-4)²=2`
`(ln(x-4)/ln(6))²=2`
`ln(x-4)/ln(6)=±sqrt2`
`ln(x-4)=±ln(6)sqrt2`
`x-4=6^(±sqrt2)`
`x=4+6^(±sqrt2)`
`x_"1"=4+6^sqrt2`
`x_"2"=4+1/(6^sqrt2)`
\0/ here's our answer!