# How do I find the value of log 100?

$\log 100 = 2$

#### Explanation:

One way we can approach log problems is to remember that

${a}^{b} = c \iff {\log}_{a} c = b$

In our question, since the value of $a$ in the right hand side log isn't specifically listed, it's assumed to be 10. So what we have is:

${a}^{b} = c \iff {\log}_{10} \left(100\right) = b$

${10}^{b} = 100 \iff {\log}_{10} \left(100\right) = b$

By observation of the left hand side, we can see that $b = 2$