Question

Which expression shows log45.9
log
4
⁡
5.9
rewritten using the change of base formula?(1 point)
Responses

log4log5.9
log
⁡
4
log
⁡
5.9
Start Fraction logarithm 4 over logarithm 5.9 End Fraction

log5.94
log
⁡
5.9
4
Start Fraction logarithm 5.9 over 4 End Fraction

ln5.9ln4
ln
⁡
5.9
ln
⁡
4
Start Fraction l n 5.9 over l n 4 End Fraction

log5.94

Answer 1

To rewrite \( \log_4(5.9) \) using the change of base formula, you can use the following formula:

\[
\log_a(b) = \frac{\log_c(b)}{\log_c(a)}
\]

where \( c \) is any positive number (commonly, we use base 10 or natural logarithm).

Using this formula, we have:

\[
\log_4(5.9) = \frac{\log(5.9)}{\log(4)} \quad \text{(using common logarithm)}
\]

or

\[
\log_4(5.9) = \frac{\ln(5.9)}{\ln(4)} \quad \text{(using natural logarithm)}
\]

From the provided options, the correct expression is:

**Start Fraction logarithm 5.9 over logarithm 4 End Fraction** (which corresponds to \(\frac{\log(5.9)}{\log(4)}\)).

So the final answer from the responses would be:

\[
\text{Start Fraction log5.9 over log4 End Fraction}
\]