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