What value is equivalent to

Question

log
2
43
to the nearest thousandth? Use the change of base formula to determine your answer.(1 point)
Responses

1.332
1.332

0.817
0.817

5.426
5.426

0.184

Answer 1

To find the value of \( \log_2{43} \) using the change of base formula, we can use the formula:

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

where \( k \) can be any positive number, commonly 10 or \( e \). We'll use base 10 for simplicity:

\[ \log_2{43} = \frac{\log_{10}{43}}{\log_{10}{2}} \]

Now, we can calculate the logarithms:

Using a calculator, we find:

• \( \log_{10}{43} \approx 1.633 \)
• \( \log_{10}{2} \approx 0.301 \)

Now we can plug in these values:

\[ \log_2{43} \approx \frac{1.633}{0.301} \approx 5.426 \]

Thus, the value of \( \log_2{43} \) to the nearest thousandth is:

5.426