Question

What are the solutions to ^log6(x^2+8)=1+log6(x)

Answer 1

x=2

x=4

Explanation:

the range is x>0

Move the expression to the left side and change it's sign to get

log6(x^2+8)-log6(x)=1

using loga(x)-loga(y) = loga (x/y) to simplify log6(x^2+8/x)=1

convert it to exponential form to get x^2+8/x=6

multiply both sides of the equation by x to get x^2+8=6x

move variable to the left

x^2-6x+8

factor out x from the expression

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

factor out x-2

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

set both equal to 0 and get x=2 x=4