How do you evaluate log 100?

3 Answers
May 19, 2015

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

Jun 11, 2017

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

Jun 12, 2017

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