Plz tell me if I solved this equation correctly!

solve for x: 8^(-x+4)=32

this is how I solved it:
i set it to -x+4=ln(32)/ln(8)
-x+4=1.66
-x=-2.33
x=2.33

It's not exact, but it's close... the exact answer would be 7/3

EDIT: So it depends on your teacher/professor... If he wants exact numbers, you'll get partial credit. If he wants approximated answers, then you're perfect.

8^(-x+4) = 32
ln 8(-x + 4) = ln(32)
(-x + 4) = ln(32) / ln(8)
-x = -4 + ( ln(32) / ln(8) )
-x = -2.33
x = 2.33

Yep you are correct.

For future reference, If you want to check whether or not you have solved equations of this type correctly.
Simply substitute x = 2.33
into:
8^(-x+4)

If you are getting 32 you are correct. If you are getting a value close to 32 but not exactly 32, do not worry, its simply because x = 2.33 is not an exact answer.

Solving it the way you solved it, you get to log_8(32) which is a rational log, 5/3. You were there, ln(32)/ln(8) = log_8(32).

8 = 2^3
32 = 2^5
(2^3)^(-x+4) = 2^5
2^(3(-x+4)) = 2^5
equating the exponents
3(-x+4) = 5
-x +4 = 5/3
x = 4 - 5/3 = 7/3

You're right!