What is the common logarithm of 54.29?

2 Answers
Sep 10, 2015

log(54.29)1.73472

Explanation:

x=log(54.29) is the solution of 10x=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:

loga(b)=logc(b)logc(a)

So:

log(54.29)=log10(54.29)=loge(54.29)loge(10)=ln(54.29)ln(10)

Sep 10, 2015

If you are using tables, you need:

Explanation:

log54.29=log(5.429×101)

  • log(5.429) +1.

From tables

log5.42=0.73400

log5.43=0.73480

5.429 is 910 of the way from 5.42 to 5.43, so we get
910=x80 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.)