Question

$4^{x+1}-7* 10^{x}+3* 25^{x}=0$

Answer 1

4^(x+1) -7*10^x +3*25^x =0

4*4^x -7*(2*5)^x +3*25^x=0

4*(2^2)^x -7*(2^x)(5^x) +3*(5^2)^x=0

4*(2^x)^2 -7*(2^x)(5^x) +3*(5^x)^2 =0

 impartim prin (2^x)(5^x)

4*[ (2^x)/(5^x)] -7 +3*[(5^x)/(2^x)] =0

4*(2/5)^x -7 +3*(5/2)^x =0

(2/5)^x =t

4t -7 +3/t =0

Inmultim cu t:

4t^2 -7t +3=0

(t-1)(4t-3)=0

t=1, (2/5)^x=1, rezulta x=0

t=3/4, (2/5)^x=3/4, x=log in baza 2/5 din 3/4