# How do you evaluate log98.2?

##### 3 Answers

#### Answer:

See explanation

#### Explanation:

These days people use calculators. Years ago log tables were used and I am not sure if I can even find my old copy of one. If you wish to use log tables I did a quick search and found this site.

https://www.wikihow.com/Use-Logarithmic-Tables

The 9 in 98.2 is counting in tens so you will have a log value starting as

My calculator gives: 1.9921 rounded to 4 decimal places.

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What is

When you see it written like this it is generally accepted that you are using what is called base10. Really it should be written as

Suppose we set

Then this is stating the condition that

EVALUATE means give value to. The value of log98.2 is

1.9921 rounded to 4 decimal places.

#### Answer:

#### Explanation:

I will calculate this to just a few significant digits, but the same method can give you more using more terms...

Use:

#ln 10 ~~ 2.302585093#

#ln(1-t) = -t-t^2/2-t^3/3-t^4/4-...#

So:

#log(98.2) = log(100*0.982)#

#color(white)(log(98.2)) = log(100)+log(1-0.018)#

#color(white)(log(98.2)) = 2+ln(1-0.018)/ln(10)#

Now:

#ln(1-0.018) = -0.018-0.018^2/2-0.018^3/3-0.018^4/4-...#

#color(white)(ln(1-0.018)) ~~ -0.018-0.000324/2#

#color(white)(ln(1-0.018)) ~~ -0.018162#

So:

#log(98.2) ~~ 2-0.018162/2.3026 ~~ 1.99211#

#### Answer:

Use

#### Explanation:

Use:

#log(2) ~~ 0.30103#

Then:

#98.2 = 100*0.982 = 100*(1-0.018) ~~ 100/(1+0.018) ~~ 100/(1.024)^(3/4) = 100/((2^10/10^3)^(3/4))#

So:

#log(98.2) ~~ log(100)-log(((2^10)/(10^3))^(3/4))#

#color(white)(log(98.2)) ~~ 2-3/4 (10log(2)-3)#

#color(white)(log(98.2)) ~~ 2-3/4 (3.0103-3)#

#color(white)(log(98.2)) ~~ 2-3/4 (0.0103)#

#color(white)(log(98.2)) ~~ 1.992#