Solve for x

27=9^-x+5

1. Use negative power rule: x^-a=1/x^a

27=1/9^x+5

2. Subtract 5 from both sides

27-5=1/9^x

3. Simplify 27-5 to 22

22=1/9^x

4. Multiply both sides by 9^x

22*9^x=1

5. Divide both sides by 22

9^x=1/22

6. Use definition of common logarithm: b^a=x if and only if log (x) = a

x=log9 (1/22)

7. Use change of base rule: logbx = (logan) / 8logab)

x = (log1/22) / (log9)

8. Use power rule: logbx^c=clogbx log1/22 - > log (22^-1) - > - log22

x = (-log22) / (log9)

9. Use power rule

Use power rule: logbx^c=clogbx, log9 - > log3^2 - > 2 log3

x = (-log22) / (2log3)

10. Your answer is, and my wish of you having a nice day : D

x = - (log22) / (2log3)

x = (approx.) - 1.41

27 = 9^-x + 5

Subtract 5 from both sides

22 = 9^-x

Log 22 = - x log 9

(Log22) / (log9) = - x

- (log22) / (log9) = x

-1.41 = x