Question

f ln11≈2.398
and ln5≈1.609
, what is ln55
? Use the Product Rule of Logarithms to solve.(1 point)
Responses

1.490
1.490

3.858
3.858

4.007
4.007

0.789

Answer 1

To find \( \ln 55 \) using the Product Rule of Logarithms, you can express 55 as the product of 11 and 5:

\[
\ln 55 = \ln(11 \times 5)
\]

According to the Product Rule of Logarithms:

\[
\ln(a \times b) = \ln a + \ln b
\]

Applying this to our expression gives:

\[
\ln 55 = \ln 11 + \ln 5
\]

Now, we can substitute the given values:

\[
\ln 11 \approx 2.398
\]
\[
\ln 5 \approx 1.609
\]

Adding these together:

\[
\ln 55 \approx 2.398 + 1.609 \approx 4.007
\]

Therefore, the correct answer is:

**4.007**