Question

Evaluate the expression log3 26 using the change of base formula.(1 point)Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.To evaluate using the change of base formula divide Response area by Response area.log3 26 ≈ Response area to the nearest thousandth. log10log26log26 3log3 26log32.9660.4728.667

Answer 1

To evaluate \( \log_3 26 \) using the change of base formula, we can use:

\[ \log_b a = \frac{\log_k a}{\log_k b} \]

For this case, we can choose \( k = 10 \) (common logarithm). Thus,

\[ \log_3 26 = \frac{\log_{10} 26}{\log_{10} 3} \]

Next, we can utilize a calculator to find \( \log_{10} 26 \) and \( \log_{10} 3 \):

• \( \log_{10} 26 \approx 1.414973 \) (approximately)
• \( \log_{10} 3 \approx 0.477121 \) (approximately)

Now we can plug these values into our formula:

\[ \log_3 26 \approx \frac{1.414973}{0.477121} \approx 2.965 \]

Now, rounding to the nearest thousandth, we get:

\[ \log_3 26 \approx 2.965 \]

To fill in the responses:

• To evaluate using the change of base formula, divide \( \log_{10} 26 \) by \( \log_{10} 3 \).
• \( \log_3 26 \approx 2.965 \).