SOLUTION: Need some help with this question! Evaluate following equation: Simplify using rules of exponents and logs: In((e^-a)(e^b)/(e^-c))^d Thanks in advance!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Need some help with this question! Evaluate following equation: Simplify using rules of exponents and logs: In((e^-a)(e^b)/(e^-c))^d Thanks in advance!       Log On


   

Question 1119237: Need some help with this question!

Evaluate following equation:
Simplify using rules of exponents and logs:
In((e^-a)(e^b)/(e^-c))^d


Thanks in advance!
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Simplifying the exponentials gives:
+e%5E%28-a%29%2Ae%5Eb+%2F+e%5E%28-c%29+=+e%5E%28b%2Bc-a%29+

Then taking ln (log base e):
+log%28e%2C+%28e%5E%28b%2Bc-a%29%29%29+=++b%2Bc-a++

Finally, raising to the d-th power:
Ans: +highlight%28+%28b%2Bc-a%29%5Ed+%29+