Questions: What is the value of the logarithm below? (Round your answer to two decimal places.) log4 12 A. 7.22 B. 0.63 C. 1.79 D. 1.08

Solution Steps

We are asked to find the value of \(\log_{4} 12\) and round it to two decimal places. The options provided are:

• A. 7.22
• B. 0.63
• C. 1.79
• D. 1.08

To compute \(\log_{4} 12\), we can use the change of base formula: \[ \log_{a} b = \frac{\log_{c} b}{\log_{c} a} \] Here, we can use base 10 or base \(e\) (natural logarithm). Let's use base 10 for simplicity: \[ \log_{4} 12 = \frac{\log_{10} 12}{\log_{10} 4} \]

Using a calculator: \[ \log_{10} 12 \approx 1.0792 \] \[ \log_{10} 4 \approx 0.6021 \]

Now, divide the two results: \[ \log_{4} 12 = \frac{1.0792}{0.6021} \approx 1.792 \]

Rounding 1.792 to two decimal places gives: \[ \log_{4} 12 \approx 1.79 \]

Final Answer