Question

How do you evaluate `log100`?

Answer 1

2

Explanation:

Using the `color(blue)"law of logarithms"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(log_b a=nhArra=b^n)color(white)(a/a)|)))`

When the log without any base indicated,is used, it usually assumes base 10.

`rArrlog_10 100=nrArr100=10^nrArrn=2`

Answer 2

`log_10 100 = 2`

Explanation:

A log expression asks a question....

If no base is shown, it is assumed to be 10

In this case `log_10 100` asks...

"What power of 10 is 100?"
"100 is which power of 10?"
"Which index of 10 will make 100?"

Log form and index form are interchangeable.

We know that `10^2 = 100` , so the answer is 2.

`log_10 100 = 2`

IN the same way:
`log_5 125 = 3 " "5^3 = 125`

`log_6 36 = 2`

`log_81 3 = 1/4 " "root4(81) = 3" or "81^(1/4) = 3`