Question

What are the solutions to log small 6 (x^2 + 8) = 1 +log small 6 (x)?

X=-2 and X=-4
X=-1 and x=8
X= 1 and X=-8
X= 2 and x=4

Answer 1

X=4 because it’s the only one tat makes sense and I checked

Answer 2

D)
`x=2` and
`x=4`

Explanation:

I assume the equation to be
`log_6(x^2+8)=1+log_6(x)`:

`log_6(x^2+8)=1+log_6(x)`

`log_6(x^2+8)-log_6(x)=1`

`log_6((x^2+8)/(x))=1`

`(x^2+8)/(x)=6`

`x^2+8=6x`

`x^2-6x+8=0`

`(x-2)(x-4)=0`

`x=2` and
`x=4`

Both solutions indeed work because you can take the logarithm of a positive number, but not a negative number, unlike the rest of the answer choices.