Answer to Question #162181 in Algebra for Gideon Silva

Question

Simplify 5^2(x-1)+5^x+2=0.04

25

25

Answer 1

$5^{2(x-1)}+5^{x+2}=0.04\newline 5^{-2}5^{2x}+5^2*5^{x}=5^{-2}$

$5^{2x}+5^4*5^{x}-1=0$

$y =5^x;y>0$

$y^2+625y-1=0$

$y= -312.5+\sqrt{97657.25}$

$x=\log_5(-312.5+\sqrt{97657.25})$

Answer:$x=\log_5(-312.5+\sqrt{97657.25})$