How do you express #log_3 42# in terms of common logs?

2 Answers
Nov 13, 2016

Answer:

#log_3 42=3.4022#

Explanation:

Common logs means logarithm with base a #10#.

Here we have been given base #3#, so let us convert it to base #10#

Let #log_3 42=x#, then #3^x=42#

and taking logarithm to base #10# on both sides, we get from tables

#xlog3=log42# and hence #x=log42/log3=1.6232/0.4771=3.4022#

Hence #log_3 42=3.4022#

Nov 13, 2016

#log_3 42#

Expand it into prime factors:
#=log_3 3 + log_3 14#
#=1+log_3 14#