Question 78707
*[Tex \large \log_5{(x+4)}+\log_5{(x-4)}=2]

Combine the logs

*[Tex \large \log_5{(x+4)(x-4)}=2]

Rewrite the expression as this:

*[Tex \large (x+4)(x-4)=5^2]
Foil and subtract 25 from both sides
*[Tex \large x^2-41=0] 

Use the quadratic formula to solve for x

*[invoke quadratic "x", 1, 0, -41 ]

Since the argument for logarithms cannot be negative, we must discard our negative answer.

So our answer is

x=6.40312423743285