How do you calculate $Log_3 63$ ?

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Answer 1 · 2016-07-16T12:02:19

$3.771$

Some calculators can work out logs with any base, but we can work it out without that function.

By definition If $log_a b= c," then " a^c = b$

Let $log_3 63 = x" then " 3^x = 63$

$log 3^x = log 63$

$xlog3 = log63$

$x = (log 63)/(log 3) = 3.771$

This is the same result we would get using the change of base law.

$log_3 63 = (log_10 63)/(log_10 3)$

$=3.771$

How do you calculate Log_3 63Log_3 63?