The Way of the Exponent

Algebra Level 2

Consider this equations:

8 x 2 x + y = 64 \dfrac{8^x}{2^{x+y}}=64 and 9 x + y 3 4 y = 243 \dfrac{9^{x+y}}{3^{4y}}=243

Find the value of 2 x y 2xy .

7 14 1 18

Natanael Flores by Natanael Flores , 31, Mexico

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

Natanael Flores
Feb 20, 2016

Simplify the fractions to obtain:

8 x = 2 x + y + 6 8^x=2^{x+y+6} -----> 2 2 x = 2 y + 6 2^{2x}=2^{y+6} and 9 x + y = 3 4 y + 5 9^{x+y}=3^{4y+5} ----> 3 2 x + 2 y = 3 4 y + 5 3^{2x+2y}=3^{4y+5}

Solving the system of equations you get y=1 and 2x=7.... so 2xy=7

3 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...