SOLUTION: How to solve for x: a^(6k) = e^(kx) Thank you!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How to solve for x: a^(6k) = e^(kx) Thank you!      Log On


   

Question 917689: How to solve for x:
a^(6k) = e^(kx)
Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+a%5E%286k%29+=+e%5E%28k%2Ax%29+
+%28+a%5E6+%29%5Ek+=+%28+e%5Ex+%29%5Ek+
Take the kth root of both sides
+a%5E6+=+e%5Ex+
+ln%28+a%5E6+%29+=+x+
+x+=+6%2Aln%28+a+%29+
------------------
check:
+a%5E%286k%29+=+e%5E%28k%2Ax%29+
+ln%28+a%5E%286k%29+%29+=+k%2Ax+
+k%2Aln%28a%5E6+%29+=+k%2A6%2Aln%28a%29+
+k%2Aln%28+a%5E6+%29+=+k%2Aln%28+a%5E6+%29+
OK