How do you solve #log_10 0.01#?

1 Answer
Rohan A.K
Feb 2, 2016

#log_10(0.01)=-2#

Explanation:

Given that we have to find the value of #log_10(0.01)#

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(10^-2)#
Now, i'm sure you know a good amount of logarithms too, so you must know that #log_nm^l=llog_nm# and that #log_n(n)=1# which means that for our problem up there is now very simple.

So, that means, in the end, #log_10(0.01)=-2log_10(10)#

You know what to do next.

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