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

Answer:

D) $x=2$ and $x=4$

Step-by-step explanation:

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

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

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

$log_6(\frac{x^2+8}{x})=1$

$\frac{x^2+8}{x}=6$

$x^2+8=6x$

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

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

$x=2$ 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.

Answer 2

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