remember
\(log(a^z)=zlog(a)\)
so
notice that 200=22255, so x cannot be a whole number
take the log base 10 of both sides
\(log_{10}(2^x)=log{10}(200)\)
\(xlog_{10}(2)=log{10}(200)\)
divide both sides by \(log_{10}(2)\)
\(x= \frac{log_{10}(200)}{log_{10}(2)}\)
if we used \(log_{2}\) instead of \(log_{10}\) we would get
\(x= log_{2}(200)\) because \(log_{a}(a^b)=b\)
