What is the common logarithm of 54.29?

2 Answers
George C.
Sep 10, 2015

#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)#

Jim H
Sep 10, 2015

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.)

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