Solve the following exponential equations. (10^x)^2 − 3(10^x) + 2 = 0

Answer:[tex]x=\frac{log(2)}{log(10)}[/tex]Step-by-step explanation:Let:[tex]y=10^{x}[/tex]So, rewritting the equation:[tex]y^{2} -3y+2=0[/tex]Factoring:[tex](y-2)(y-1)=0[/tex]Therefore:[tex]y=2\hspace{5}or\hspace{5}y=1[/tex]Substitute back for [tex]y=10^{x}[/tex]for y=2Taking the logarithm base 10 of both sides:[tex]x=\frac{log(2)}{log(10)}[/tex]for y=1Taking the logarithm base 10 of both sides and adding 1 to both sides:[tex]log(1)+x=\frac{log(2)}{log(10)}[/tex][tex]log(1)=0[/tex]so:[tex]x=\frac{log(2)}{log(10)}[/tex]Hence:[tex]x=\frac{log(2)}{log(10)}[/tex]