Question

How do you evaluate `log 100`?

Answer 1

`log100=2`

To evaluate this you use the definition of a logarithm.
`log_ab=c iff a^c=b`

You also have to assume that if no base `b` is written then the base is `10`

So in the example you have `log_(10)100=c iff 10^c=100`.

Now you can easily find that `c=2`, because `10^2=10*10=100`.

So the answer is
`log100=log_(10)100=2`

Answer 2

`log100=2`

Explanation:

`log100=2` because it can be denoted as

`log100 = log(10 * 10) = log10+log10`

Keep in mind that when there is no base written, it is assumed to be a base of `10`. Applying the rule of `log x=1`, you have `log10=1`.

Then that means

`log10+log10=1 + 1 = 2`

Also, you can use the power rule.

`log 100 = log(10^2) =2*log10`

which is equal to

`2*1=2`

Answer 3

`10^2 = 100, " ":. log_10 100 =2`

Explanation:

It might help to compare the two notations:

Index form and log form.`" "` They are interchangeable.

`a^b = c hArr loga_c =b`

Index form makes a statement:

`10^1 = 10," " 10^2 = 100," "10^3 = 1000`

Log form asks a question.....

`log_10 100 =???`

"What power of `10` will give `100`?

`log_10 100 =2`

In the same way..

`log_4 16 = 2" because " 4^2 = 16`

`log_3 27 = 3" because " 3^3=27`

`log_2 32 = 5" because " 2^5=32`