Question 1202791
Find x if 5^(2x+1) +5^(2x)= 3750

{{{5^(2x+1) +5^(2x)= 3750}}}


{{{5^(2x+1) = 5^(2x) * 5^1 }}}   (a^m*a^n= a^(m+n)

we get

5*5^(2x) +5^(2x)= 3750


5^(2x)*(5+1) 3750

5^2x = 3750/5 = 625

5^(2x) = 5^4= 5^(2*2)

Base same compare indices

2x=4

x=2