SOLUTION: 2^(log base 3 of 5) - 5^(log base 3 of 2)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 2^(log base 3 of 5) - 5^(log base 3 of 2)      Log On


   

Question 1006783: 2^(log base 3 of 5) - 5^(log base 3 of 2)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
2%5Elog%283%2C5%29%22%22-%22%225%5Elog%283%2C2%29

Let's take the log base 3 of each of those 
two expressions which are subtracted:

Take the log base 3 of 2%5Elog%283%2C5%29

log%283%2C2%5Elog%283%2C5%29%29

log%283%2C5%29log%283%2C2%29

Take the log base 3 of 5%5Elog%283%2C2%29

log%283%2C5%5Elog%283%2C2%29%29

log%283%2C2%29log%283%2C5%29

Since the base 3 logs of 2%5Elog%283%2C5%29 and 5%5Elog%283%2C2%29
are equal, they are also equal and so their difference is 0.

Answer: 0 

Edwin