How do you solve log_10 0.01?

Feb 2, 2016

${\log}_{10} \left(0.01\right) = - 2$

Explanation:

Given that we have to find the value of ${\log}_{10} \left(0.01\right)$

Now, I believe you're familiar with exponents, powers and bases and about the number system being based on the powers of $10$.
So you'd obviously we can write that $0.01$ is the same as ${10}^{-} 2$

So writing that instead of $0.01$, we get that the problem is a bit easier, ${\log}_{10} \left({10}^{-} 2\right)$
Now, i'm sure you know a good amount of logarithms too, so you must know that ${\log}_{n} {m}^{l} = l {\log}_{n} m$ and that ${\log}_{n} \left(n\right) = 1$ which means that for our problem up there is now very simple.

So, that means, in the end, ${\log}_{10} \left(0.01\right) = - 2 {\log}_{10} \left(10\right)$

You know what to do next.