How do you evaluate #log100#?

2 Answers
Aug 22, 2016

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#

Aug 22, 2016

#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#