SOLUTION: Suppose a and b are positive real numbers for which {{{ log( a, b)=log( b, a) }}}. If neither a nor b is 1 and a does not equal b, find the value of ab.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Suppose a and b are positive real numbers for which {{{ log( a, b)=log( b, a) }}}. If neither a nor b is 1 and a does not equal b, find the value of ab.       Log On


   

Question 761494: Suppose a and b are positive real numbers for which +log%28+a%2C+b%29=log%28+b%2C+a%29+. If neither a nor b is 1 and a does not equal b, find the value of ab.
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+a%2C+b%29=log%28+b%2C+a%29+
+log%28a%29%2Flog%28b%29=log%28+b%29%2Flog%28+a%29+
%28log+%28a%29%29%5E2=%28log+%28b%29%29%5E2%0D%0A
%28log+%28a%29%29%5E2-%28log+%28b%29%29%5E2=0%0D%0A
%28log+%28a%29-log%28b%29%29%28log+%28a%29%2Blog%28b%29%29=0%0D%0A

and by our initial conditions...
%28log+%28a%29%2Blog%28b%29%29=0
or...

log%28ab%29=0

10%5Elog%28ab%29=10%5E0

ab=1

:)