Question 1088599
3^(-3x) = 81
log(3^(-3x)) = log(81)
Since the logarithm of a number raised to a power is the power times the logarithm of the number:
((-3)x)(log(3)) = log(81)
(-3)x = log(81)/log(3)
(-3)x = log_3(81) = 4
x = 4/-3 = -1.3333
Well, I'm afraid I haven't been of any help since I got the same answer you got and obviously your teacher is looking for a different answer. But I have solved the problem correctly, so whoever is telling you that this is the wrong answer is, in my view, making a mistake. S/he needs to work the problem so s/he can see that the answer book they have is incorrect. Good luck.