Examples of Math Problems: Suppose a and b are positive real numbers for which . If neither a nor b is 1 and a does not equal b, find the value of ab.

Saturday, June 29, 2013

Suppose a and b are positive real numbers for which . If neither a nor b is 1 and a does not equal b, find the value of ab.

+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

%28log+%28a%29%2Blog%28b%29%29=0

or...

log%28ab%29=0

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

ab=1

:)

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