Question

Which of the following expressions are equal to 3? Select all that apply.
(2 points)
Responses

natural log e cubed
Image with alt text: natural log e cubed

ln 3
ln 3

log subscript 5 baseline 15
Image with alt text: log subscript 5 baseline 15

log subscript 4 baseline 64
Image with alt text: log subscript 4 baseline 64

log 1,000
log 1,000

log 300
log 300

Answer 1

Let's evaluate each expression to determine which ones are equal to 3:

1. **Natural log of e cubed (ln(e³))**:
- Using the property of logarithms, ln(e^x) = x, we have ln(e³) = 3.
- So this is equal to 3.

2. **ln(3)**:
- This is just the natural logarithm of 3. It is not equal to 3.

3. **log₅(15)**:
- We need to determine if 5^3 = 15.
- 5^3 = 125, not 15. So log₅(15) is not equal to 3.

4. **log₄(64)**:
- We find if 4^3 = 64.
- 4^3 = 64, so log₄(64) = 3. Therefore, this is equal to 3.

5. **log(1,000)** (base 10):
- We check if 10^3 = 1,000.
- 10^3 = 1,000, so log(1,000) = 3. This is equal to 3.

6. **log(300)** (base 10):
- We check if 10^3 = 300.
- 10^3 = 1,000, not 300. Therefore, log(300) is not equal to 3.

### Conclusion:
The expressions that are equal to 3 are:
- Natural log of e cubed (ln(e³))
- log₄(64)
- log(1,000)