Question

Given that `log 7623 ~~ 3.8821`, what logarithms are `0.8821`, `7.8821`, `1.8821` ?

Answer 1

`0.8821 ~~ log(7.623)`

`7.8821 ~~ log(76230000)`

`1.8821 ~~ log(76.23)`

Explanation:

Note that:

`log 10^n = n`

`log ab = log a + log b" "` for `a, b > 0`

`log (a/b) = log a - log b" "` for `a, b > 0`

So:

`log a * 10^n = log a + log 10^n = log a + n`

Putting `a=7623`, we find:

a. `0.8821 = 3.8821 - 3 ~~ log 7623 - log 10^3 = log (7632/10^3) = log 7.623`

b. `7.8821 = 3.8821 + 4 ~~ log 7623 + log 10^4 = log (7623 * 10^4) = log 76230000`

c. `1.8821 = 3.8821 - 2 ~~ log 7623 - log 10^2 = log (7623/100) = 76.23`