Question

8^(-x+14)=16^x

Answer 1

\[8=2^3 ; 16=2^4\]

Answer 2

You need to convert the base to the same number. So, in this case, write 8 and 16 as powers of 2.

Answer 3

\[2^{3(-x+14)}=2^{4x}\]

Answer 4

okay and then what do i do next?

Answer 5

since the bases are same on both side
set exponent parts equal and solve for x

Answer 6

That means:
3(−x+14) = 4x
Now, solve for x.

Answer 7

8^(-x+14)=16^x
8^(14-x)=16^x
(2^3)^(14-x)=(2^4)^x
2^42-3x=2^4x
since bases are the same equate the index
42-3x=4x
-3x-4x=-42
-7x/-7=-42/-7
x=6