Question

How do I evaluate a log when the argument is in a fraction?

Answer 1

Step-by-step explanation:

Given that

`\begin{gathered} \log_43\approx0.7925 \\ find \\ \log_4((1)/(9)) \end{gathered}`

Apply the law of fractional indices below

`(1)/(a)=a^(-1)`

By applying the law, we will have that

`\begin{gathered} (1)/(9)=9^(-1) \\ recall: \\ 9=3^2 \\ 9^(-1)=3^(-2) \end{gathered}`

By rewriting the expression, we will have

Apply the logarithmi law of exponents below

`\log_ba^c=c\log_ba`
`\begin{gathered} \log_4(3^(-2))=-2\log_43 \\ -2\log_43=-2(0.7925) \\ =-1.5850 \end{gathered}`

Hence,

The final answer to 4 decimal places is

`-1.5850`