Solve for x:

Question

1.) ln√x-8=5

2.) log2x+log2(x+2)=log2(x+6)

Answer 1

ln√x-8=5
ln√x=13
√x = e^13
x = e^26

log2x+log2(x+2)=log2(x+6)
log2(x(x+2)) = log2(x+6)
x(x+2) = x+6
x^2+2x = x+6
x^2+x-6 = 0
(x-2)(x+3) = 0
x = 2 or -3

But, log2(x) is not defined for x <= 0, so

x=2 is the only solution

check:

log2(2)+log2(2+2) = log2(2+6)
1+2 = 3