Question

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

3.858
3.858

0.789
0.789

4.007
4.007

1.490
1.490

Answer 1

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

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

According to the Product Rule of Logarithms:

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

Therefore:

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

Substituting the approximate values given:

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

Now, let's perform the addition:

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

Thus, the approximate value of \( \ln 55 \) is:

\[
\boxed{4.007}
\]