Question

I need help with this.

Answer 1

9514 1404 393

Answer:

  6/(2+k)

Step-by-step explanation:

The change of base formula is ...

  $\log_a(b)=\dfrac{\log(b)}{\log(a)}$

Using this, we can take the logarithm base 2 in the change of base formula for the given expression.

  $\log_{20}(64)=\dfrac{\log_2(64)}{\log_2(20)}=\dfrac{\log_2(2^6)}{\log_2(2^2\cdot5)}\\\\=\dfrac{6}{\log_2(2^2)+\log_2(5)}=\boxed{\dfrac{6}{2+k}}$

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In addition to the change of base formula, the usual rules of logarithms apply.

  $a^b=m\ \longleftrightarrow \ \log_a(m)=b\\\log(ab)=\log(a)+\log(b)$