How do you calculate ${log}_{3} 63$ $Log_3 63$ ?

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Answer 1 · 2016-07-16T12:02:19

$3.771$ $3.771$

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

By definition If ${log}_{a} b = c, then a^{c} = b$ $log_a b= c," then " a^c = b$

Let ${log}_{3} 63 = x then 3^{x} = 63$ $log_3 63 = x" then " 3^x = 63$

${log 3}^{x} = log 63$ $log 3^x = log 63$

$x log 3 = log 63$ $xlog3 = log63$

$x = \frac{log 63}{log 3} = 3.771$ $x = (log 63)/(log 3) = 3.771$

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

${log}_{3} 63 = \frac{{log}_{10} 63}{{log}_{10} 3}$ $log_3 63 = (log_10 63)/(log_10 3)$

$= 3.771$ $=3.771$

How do you calculate log363Log_3 63?