Asked by What is 1n if
Rewrite log4 35 using the change of base formula
Answers
Answered by
GPT-4o mini
To rewrite \(\log_4 35\) using the change of base formula, you can use the following formula:
\[
\log_a b = \frac{\log_c b}{\log_c a}
\]
where \(a\), \(b\), and \(c\) are any positive numbers, and \(c\) is the new base you want to use.
For example, if you want to change the base to 10, the expression becomes:
\[
\log_4 35 = \frac{\log_{10} 35}{\log_{10} 4}
\]
If you want to change the base to \(e\) (natural logarithm), it would look like this:
\[
\log_4 35 = \frac{\ln 35}{\ln 4}
\]
You can choose any base for \(c\), such as 2 or 10, depending on what is most convenient for your calculations.
\[
\log_a b = \frac{\log_c b}{\log_c a}
\]
where \(a\), \(b\), and \(c\) are any positive numbers, and \(c\) is the new base you want to use.
For example, if you want to change the base to 10, the expression becomes:
\[
\log_4 35 = \frac{\log_{10} 35}{\log_{10} 4}
\]
If you want to change the base to \(e\) (natural logarithm), it would look like this:
\[
\log_4 35 = \frac{\ln 35}{\ln 4}
\]
You can choose any base for \(c\), such as 2 or 10, depending on what is most convenient for your calculations.