A problem by Morgan Blake

Level pending

Given that 4 x = 9 4^{x}=9 and 9 y = 256 9^{y}=256 , what is the value of x y xy ?


The answer is 4.

Morgan Blake by Morgan Blake , 25, United Kingdom

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Tom Engelsman
Sep 1, 2018

Substituting the first equation into the second gives:

9 y = ( 4 x ) y = 256 ; 9^y = (4^x)^{y} = 256;

or 4 x y = 4 4 4^{xy} = 4^4 ;

or x y = 4 . \boxed{xy = 4}.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...