Question

How do you evaluate log98.2?

Answer 1

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 `1.0` plus some decimal that you put after the decimal point.

My calculator gives: 1.9921 rounded to 4 decimal places.
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What is `log98.2` actually saying?

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 `log_10 98.2`

Suppose we set `log98.2=x`

Then this is stating the condition that `10^x=98.2`

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

1.9921 rounded to 4 decimal places.

Answer 2

`log(98.2) = log(100)-ln(1-0.018)/ln(10) ~~ 1.99211`

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 3

Use `log(2) ~~ 0.30103` to find `log(98.2) ~~ 1.992`

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`