Watch the video and then solve the problem given below.
Click here to watch the video.
Use properties of logarithms to expand the logarithmic
expression as much as possible. Evaluate logarithmic
expressions without using a calculator if possible.

Ask by Nunez Craig. in the United States

Mar 23,2025

Question

Watch the video and then solve the problem given below.
Click here to watch the video.
Use properties of logarithms to expand the logarithmic
expression as much as possible. Evaluate logarithmic
expressions without using a calculator if possible.

Ask by Nunez Craig. in the United States

Mar 23,2025

UpStudy AI · Accepted Answer

We start with the logarithmic expression:
$$
\ln \left(\frac{e^{9}}{14}\right)
$$

**Step 1: Apply the Quotient Rule**

The logarithm of a quotient is the difference of the logarithms:
$$
\ln \left(\frac{e^{9}}{14}\right) = \ln(e^9) - \ln(14)
$$

**Step 2: Simplify $$\ln(e^9)$$**

Using the property $$\ln(e^x) = x$$, we have:
$$
\ln(e^9) = 9
$$

**Step 3: Combine the Results**

Substituting back, the expression becomes:
$$
9 - \ln(14)
$$

Thus, the expanded form is:
$$
\ln \left(\frac{e^{9}}{14}\right) = 9 - \ln(14)
$$
$$ \ln \left(\frac{e^{9}}{14}\right) = 9 - \ln(14) $$