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)

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

$= 1.201$

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