How do you calculate Log_3 63log363?

1 Answer
Jul 16, 2016

3.7713.771

Explanation:

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 = blogab=c, then ac=b

Let log_3 63 = x" then " 3^x = 63log363=x then 3x=63

log 3^x = log 63log3x=log63

xlog3 = log63xlog3=log63

x = (log 63)/(log 3) = 3.771x=log63log3=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)log363=log1063log103

=3.771=3.771