Question

Resolva a seguinte equação exponencial:
a) 25 . 9^x + 16 . 15^x = 9 . 25^x

Answer 1

$25\cdot9^x+16\cdot15^x=9\cdot25^x\\\\5^2\cdot3^{2x}+2^4\cdot3^x\cdot5^x=3^2\cdot5^{2x}\\\\3^x\cdot(5^2\cdot3^x+2^4\cdot5^x)=3^2\cdot5^{2x}$
 
 Igualemos os expoentes do fator 3,

$x=2$


 Por conseguinte,

$(5^2\cdot3^x+2^4\cdot5^x)=5^{2x}\\\\5^2\cdot3^2+2^4\cdot5^2=5^{2\cdot2}\\\\5^2(3^2+2^4)=5^4\\\\5^2\cdot(25)=5^4\\\\5^4=5^4$
 

 De fato, $\boxed{x=2}$