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

1 answer

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:

\[ \boxed{4.007} \]