remember
[tex]log(a^z)=zlog(a)[/tex]
so
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]
