Question

which expression shows \\(\log_{4} 35\\) rewritten using the change of base formula? (1 point)\
\\(\circ\\) \\(\log \frac{4}{35}\\)\
\\(\circ\\) \\(\frac{\log 35}{\log 4}\\)\
\\(\circ\\) \\(\log \frac{35}{4}\\)\
\\(\circ\\) \\(\frac{\log 4}{\log 35}\\)

Explanation:

Step1: Recall change of base formula

The change of base formula for logarithms is \(\log_{b}a=\frac{\log_{c}a}{\log_{c}b}\), where \(c>0,c
eq1\).

Step2: Apply the formula to \(\log_{4}35\)

Here, \(b = 4\), \(a=35\), and we can use \(c\) as the common logarithm base (base 10) or natural logarithm base (base \(e\)). So applying the formula, we get \(\log_{4}35=\frac{\log 35}{\log 4}\) (using base 10 logarithms, but it could also be \(\frac{\ln 35}{\ln 4}\)).

Answer:

\(\frac{\log 35}{\log 4}\) (corresponding to the option: \(\boldsymbol{\frac{\log 35}{\log 4}}\))