How do you calculate #log_7 8.34# with a calculator?

1 Answer
Alan N.
Aug 23, 2016

#log_7 8.34~=1.09001#

Explanation:

Using the relationship:
#log_b x = log_a x/ log_a b#

In this example # x = 8.34 and b=7 #
and let #a=10# (to allow the calculation on a simple scientific calculator.)

Hence: #log_7 8.34 = log_10 8.34/log_10 7#

#~= 0.92117/0.84510#

#~= 1.09001#

NB: To check result #7^1.09001 = 8.34# to 2 decimals

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