Indices problem 1 by Dhaval Furia

Algebra Level pending

If 5 x − 3 y = 13438 5^{x} - 3^{y} = 13438 and 5 x − 1 + 3 y + 1 = 9686 5^{x-1} + 3^{y+1} = 9686 , what is x + y x + y equals to?


The answer is 13.

Dhaval Furia by Dhaval Furia , 26, India

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

Chew-Seong Cheong
May 22, 2020

Given that { 5 x − 3 y = 13438 . . . ( 1 ) 5 y − 1 + 3 x + 1 = 9686 . . . ( 2 ) \begin{cases} 5^x - 3^y = 13438 & ...(1) \\ 5^{y-1} + 3^{x+1} = 9686 & ...(2) \end{cases}

5 × ( 2 ) − ( 1 ) : 16 ⋅ 3 y = 34992 3 y = 2187 y = 7 \begin{aligned} 5\times(2) - (1): \quad 16\cdot 3^y & = 34992 \\ 3^y & = 2187 \\ y & = 7 \end{aligned}

( 1 ) : 5 x − 2187 = 13438 5 x = 15625 ⟹ x = 6 \begin{aligned} (1): \quad 5^x - 2187 & = 13438 \\ 5^x & = 15625 \\ \implies x & = 6 \end{aligned}

Therefore x + y = 7 + 6 = 13 x+y = 7+6 = \boxed{13} .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...