Question

5^x+5^(x+2)=2^(x+1)+2^(x+2)

Answer 1

$5^x+5^{x+2}=2^{x+1}+2^{x+2} \ 5^x+5^xcdot5^2}=2^xcdot2}+2^xcdot2^2 \ 5^x+25cdot5^x=2cdot2^x+4cdot2^x \ 26cdot5^x=6cdot2^x \ ( frac{5}{2})^x= frac{6}{26} \ ( frac{5}{2})^x= frac{3}{13} \ (frac{5}{2})^x= (frac{5}{2})^{log_ frac{5}{2} frac{3}{13}} \ x= log_ frac{5}{2} frac{3}{13}$