9514 1404 393
Answer:
6/(2+k)
Step-by-step explanation:
The change of base formula is ...
[tex]\log_a(b)=\dfrac{\log(b)}{\log(a)}[/tex]
Using this, we can take the logarithm base 2 in the change of base formula for the given expression.
[tex]\log_{20}(64)=\dfrac{\log_2(64)}{\log_2(20)}=\dfrac{\log_2(2^6)}{\log_2(2^2\cdot5)}\\\\=\dfrac{6}{\log_2(2^2)+\log_2(5)}=\boxed{\dfrac{6}{2+k}}[/tex]
__
In addition to the change of base formula, the usual rules of logarithms apply.
[tex]a^b=m\ \longleftrightarrow \ \log_a(m)=b\\\log(ab)=\log(a)+\log(b)[/tex]
