Question

5^{2x-5}+25^{x-1}=126

Answer 1

$5^{2x-5} + 25^{x-1} = 126,$
$frac{5^{2x}}{5^5} + (5^2)^{x-1} = 126$
$frac{5^{2x}}{5^5} + 5^{2cdot (x-1)} = 126$
$frac{5^{2x}}{5^5} + 5^{2x-2} = 126$
$frac{5^{2x}}{5^5} + frac{5^{2x}}{5^2} = 126$
$frac{5^{2x}}{5^2} cdot ( frac{1}{5^3} + 1 ) = 126$
$frac{5^{2x}}{25} cdot frac{1+5^3}{5^3} = 126$
$frac{5^{2x}}{25} cdot frac{126}{5^3} = 126$
$5^{2x} = 5^3 cdot 25 = 5^5$
$2x = 5$
$x = 5/2 = 2,5$