Step by step
The question
Question: work out log 0.01.
A log with no small number is base 10.
log 0.01
So it is log base 10.
log = log10
0.01 is 1/100.
It is easier to work with as a fraction.
0.01 = 1100
1 What the log asks
A log is a power.
log 0.01 asks: 10 to what power is 1/100?
a log is a power
10 to the power what is 1/100?
10? = 1100
2 Find the power
100 is 10².
A minus power means 1 over.
So 1/10² is 10⁻².
10 × 10 = 100
1102 = 10−2
So the power is −2.
10−2 = 1100
So log 0.01 = −2.
log 0.01 = −2
Let's look back.
First: what the log asks.
Last: find the power.
Answer
log 0.01 = −2