4 of 54 of 5 Items

Question
Which expression shows log435
rewritten using the change of base formula?(1 point)
Responses

log435
logarithm Start Fraction 4 over 35 End Fraction

log354
logarithm Start Fraction 35 over 4 End Fraction

log4log35
Start Fraction logarithm 4 over logarithm 35 End Fraction

log35log4

1 answer

The change of base formula for logarithms states that:

\[ \log_b(a) = \frac{\log_k(a)}{\log_k(b)} \]

for any positive \(k\), where \(a\) and \(b\) are the values of the logarithm and the base, respectively.

To rewrite \(\log_4(35)\) using the change of base formula, you can use the common logarithm (base 10) or the natural logarithm (base \(e\)). The expression becomes:

\[ \log_4(35) = \frac{\log(35)}{\log(4)} \]

Thus, the correct rewriting of \(\log_4(35)\) using the change of base formula is:

\[ \frac{\log(35)}{\log(4)} \quad \text{or} \quad \frac{\log 35}{\log 4} \]

From the provided options, the correct response that matches this is:

\[ \text{Start Fraction logarithm 35 over logarithm 4 End Fraction} \]

So, the correct choice is:

log35/log4.