How do you calculate ${log}_{9} 14$ $log_9 14$ with a calculator?

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Answer 1 · 2016-09-27T18:21:13

$1.201$ $1.201$

Log form and index form are interchangeable.

${log}_{a} b = c \Leftrightarrow a^{c} = b$ $log_a b = c " " hArr " " a^c = b$

Let ${log}_{9} 14 = x \to 9^{x} = 14$ $log_9 14 = x " "rarr 9^x = 14$

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

${log 9}^{x} = log 14 \leftarrow$ $log 9^x = log14" "larr$ log power law

$x log 9 = log 14 \leftarrow isolate x$ $xlog9 = log14" "larr" isolate " x$

$x = \frac{log 14}{log 9} \leftarrow$ $x = log14/log9 " "larr$ use a calculator.

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

$x = 1.201$ $x = 1.201$

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

${log}_{a} b = \frac{{log}_{c} b}{{log}_{c} a} \leftarrow$ $log_a b = (log_c b)/(log_c a)" "larr$ (c can be any base)

${log}_{9} 14 = \frac{{log}_{10} 14}{{log}_{10} 9}$ $log_9 14 = (log_10 14)/(log_10 9)$

$= 1.201$ $= 1.201$

How do you calculate log914log_9 14 with a calculator?