SOLUTION: If log a=.5, log b=.3, and log c= 16, solve the following equation for x. a^x b^x=c Can somebody please try to guide me in the right direction? I do not want an answer to the

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: If log a=.5, log b=.3, and log c= 16, solve the following equation for x. a^x b^x=c Can somebody please try to guide me in the right direction? I do not want an answer to the      Log On


   

Question 554086: If log a=.5, log b=.3, and log c= 16, solve the following equation for x.
a^x b^x=c
Can somebody please try to guide me in the right direction? I do not want an answer to the problem, but only some guidance where to start.
Thanks!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+a%5Ex%2Ab%5Ex+=+c+
Suppose I say +d+=+a%5Ex+ and +e+=+b%5Ex+
Then I have +d%2Ae+=+c+.
It is true that +log%28%28+d%2Ae+%29%29+=+log%28d%29+%2B+log%28e%29+
Take the log of both sides of the original equation
+log%28%28+a%5Ex%2Ab%5Ex+%29%29+=+log%28%28+c+%29%29+
+log%28%28+a%5Ex+%29%29+%2B+log%28%28+b%5Ex+%29%29+=+log%28%28+c+%29%29+
+x%2Alog%28%28+a+%29%29+%2B+x%2Alog%28%28+b+%29%29+=+log%28%28+c+%29%29+
+x%2A%28+log%28a%29+%2B+log%28b%29+%29+=+log%28%28+c+%29%29+
+x%2A%28+.5+%2B+.3+%29+=+16+
+x+=+16+%2F+.8+
+x+=+20+
Sorry, I did the whole thing.