math question...........please help?

Question

solve for x:

^ 2 = squared

log( x ^ 2 - 16 ) - 1 = log ( x + 4 )

Answer 1

log(x^2 - 16) - 1 = log(x + 4)

First, factor x^2 - 16 as a difference of squares.

log[ (x - 4)(x + 4) ] - 1 = log(x + 4)

Use the log property log(ab) = log(a) + log(b).

log(x - 4) + log(x + 4) - 1 = log(x + 4)

Subtract log(x + 4) both sides, eliminating them.

log(x - 4) - 1 = 0

Move the 1 to the right hand side.

log(x - 4) = 1

Change this to exponential form.

10^1 = x - 4

Now, solve for x normally.

10 = x - 4
14 = x.