Evaluate natural log start root start fraction e superscript 7 baseline over e superscript 5 baseline end fraction end root.

Question

(1 point)
Responses

1
1

2
2

e
e

e squared
Image with alt text: e squared

Answer 1

To evaluate the expression \(\ln\left(\sqrt{\frac{e^7}{e^5}}\right)\), we can simplify it step by step.

1. First, simplify the fraction inside the square root: \[ \frac{e^7}{e^5} = e^{7-5} = e^2. \]

2. Next, take the square root: \[ \sqrt{e^2} = e. \]

3. Finally, evaluate the natural logarithm: \[ \ln(e) = 1. \]

Therefore, the final result is: \[ \ln\left(\sqrt{\frac{e^7}{e^5}}\right) = 1. \]

The answer is 1.