Solve the equations, and checks for extraneous solutions.

Hello,

15:
3^(4x-2)=9^(x-4)
==>4x-2=2(x-4)
==>2x=-6
==>x=-3

Proof:
 3^(4*(-3)-2)=3^(-14)
9^(-3-4)=9^(-7)=3^(-14)

16:
Log is in base 10

2^x=70
==> x Log 2= Log 70
==>x=Log 70/ Log 2
==>x=6.129830...

17:

log2 = log in base 2

log2 x / log2 3=4
==>x=2^(4 log2 3)
==>x=(2^(log2 3))4
==>x=3^4
==>x=81

18:
log3 (x-2)+log3 x=1
log3 ((x-2)*x) =1
==> (x-2)*x=3

==>x²-2x-3=0
==>(x=3) or (x=-1)

If x=3
log3 (3-2)=log3 (-1) =0
log3 3=1
and 0+1=1

if x=-1
log3  (-1-2)=log3 (-3) exclude