Question

What is the common logarithm of 54.29?

Answer 1

`log(54.29) ~~ 1.73472`

Explanation:

`x = log(54.29)` is the solution of `10^x = 54.29`

If you have a natural log (`ln`) function but not a common `log` function on your calculator, you can find `log(54.29)` using the change of base formula:

`log_a(b) = log_c(b)/log_c(a)`

So:

`log(54.29) = log_10(54.29) = log_e(54.29)/log_e(10) = ln(54.29)/ln(10)`

Answer 2

If you are using tables, you need:

Explanation:

`log54.29 = log(5.429 xx 10^1)`

• log(5.429) +1.

From tables

`log5.42 = 0.73400`

`log5.43 = 0.73480`

`5.429` is `9/10` of the way from `5.42 " to " 5.43`, so we get
`9/10 = x/80` so `x=72`

by linear interpolation,

`log(5.429) = 0.74372`

So
`log(54.29) = 1.74372`

(I'm using `=` rather than `~~` in each case.)