How do you calculate #log_9 14# with a calculator?

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Answer 1 · 2016-09-27T18:21:13

#1.201#

Log form and index form are interchangeable.

#log_a b = c " " hArr " " a^c = b#

Let #log_9 14 = x " "rarr 9^x = 14#

As #x# is in the index, use logs to solve.

#log 9^x = log14" "larr# log power law

#xlog9 = log14" "larr" isolate " x#

#x = log14/log9 " "larr# use a calculator.

(if no base is given, it is implied it is base 10)

#x = 1.201#

The same result would have been obtained from using the "Change of base law"

#log_a b = (log_c b)/(log_c a)" "larr# (c can be any base)

#log_9 14 = (log_10 14)/(log_10 9)#

#= 1.201#