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...
$$2 / \log2;$$ $$10 / \log2 ; $$ $$50 / \log2 ; $$ $$100 / \log2 ; $$
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.
No that is wrong. The solution should be $\frac{\log(100)}{\log(2)}$.
To calculate the log of x to the basis b you can use this formula:
$$ \log_b(x) = \frac{\log(x)}{\log(b)} $$
By definition, $2^{^2log(a)}=a$. Applying this to $a=100$ results in $2^x=2^{^2log(100)}$, thus $x=^2log(100)$. This can also be written as $x=\frac{log(100)}{log(2)}$. Notice that $log(100)=2$, thus $x=\frac{2}{log(2)}$
