Question 1148189
<br>
By inspection....<br>
We need to add two powers of 5 to get a sum of 150.  Since that sum is a whole number, the powers have to be integers.<br>
5^1 = 5
5^2 = 25
5^3 = 125<br>
25+125 = 150; so x and y are 2 and 3.<br>
Then, since we are told that x-y=1, x is 3 and y is 2.<br>
If you need an algebraic solution....<br>
x-y=1 --> x = y+1<br>
Then<br>
{{{5^x+5^y=150}}}
{{{5^(y+1)+5^y = 150}}}
{{{5*(5^y)+5^y = 150}}}
{{{6*5^y = 150}}}
{{{5^y = 25}}}
{{{y = 2}}}
{{{x = y+1 = 3}}}<br>