notice that 200=2*2*2*5*5, so x cannot be a whole number
take the log base 10 of both sides
[tex]log_{10}(2^x)=log{10}(200)[/tex] [tex]xlog_{10}(2)=log{10}(200)[/tex] divide both sides by [tex]log_{10}(2)[/tex] [tex]x= \frac{log_{10}(200)}{log_{10}(2)} [/tex]
if we used [tex]log_{2}[/tex] instead of [tex]log_{10}[/tex] we would get [tex]x= log_{2}(200) [/tex] because [tex]log_{a}(a^b)=b [/tex]
