SOLUTION: Can you prove the Property: Loga^x= log10^x/log10^a

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Can you prove the Property: Loga^x= log10^x/log10^a      Log On


   

Question 72498: Can you prove the Property: Loga^x= log10^x/log10^a
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
prove the Property: Loga^x= log10^x/log10^a
-----------
Let log(base a)x = W
Then a^W = x
Take the log(base 10) of both sides to get:
wlog(base 10)a = log(base 10)x
Substitute for w to get:
[log(base a)x][log(base 10)a = log(base 10)x
Divide both sides by log(base 10)a to get:
log(base a)x = [log(base 10)x]/[log(base 10)a
--------
Cheers,
Stan H.