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=2
Taking the logarithm base 10 of both sides:
[tex]x=\frac{log(2)}{log(10)}[/tex]
for y=1
Taking 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]
