If $2^x$ (2 to the power of x) $= 100$, what is $x$?
I got $100/\log2$. Is that correct? I know how I solved it but now I don't get how I did and why I did what I did.
The choices were…
$$2 / \log2;$$
$$10 / \log2 ; $$
$$50 / \log2 ; $$
$$100 / \log2 ; $$
Best Answer
The answer should be $2/\log 2$.
$$\begin{align} 2^x & =100\\ \log 2^x & =\log 100\\ x\log 2 & = 2\\ x &=\frac2{\log 2} \end{align}$$
Remember that $\log x$ answers the question "What power of 10 is x?" So, $\log100=2$ Also a useful propery of $\log$ is $\log x^a=a\log x$. This explains how I got the third line.