SOLUTION: Hi. My name is Allen and I'm having difficulty solving this log problem. I've tried different solutions, such as 7^(10^a), etc. Express 10^a as a power of 7. That is, if 10^a=

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi. My name is Allen and I'm having difficulty solving this log problem. I've tried different solutions, such as 7^(10^a), etc. Express 10^a as a power of 7. That is, if 10^a=      Log On


   

Question 710330: Hi. My name is Allen and I'm having difficulty solving this log problem. I've tried different solutions, such as 7^(10^a), etc.
Express 10^a as a power of 7.
That is, if 10^a=7^x, then x= ________
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
10%5Ea=7%5Ex
Taking base 10 logarithms on both sides of the equal sign:
a=log%287%5Ex%29 --> a=xlog%287%29 --> x=a%2Flog%287%29
10^a=7^(a/log(7))