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
To determine which expressions are equal to 3, we can evaluate each logarithm expression.
1. natural log e cubed = ln(e^3) = 3, so this expression is equal to 3.
2. ln 3 = natural logarithm of 3 ≈ 1.0986, so this expression is not equal to 3.
3. log subscript 5 baseline 15 = log base 5 of 15 ≈ 1.6826, so this expression is not equal to 3.
4. log subscript 4 baseline 64 = log base 4 of 64 = 3, so this expression is equal to 3.
5. log 1,000 = log base 10 of 1,000 = 3, so this expression is equal to 3.
6. log 300 = log base 10 of 300 ≈ 2.4771, so this expression is not equal to 3.
Therefore, the expressions that are equal to 3 are:
- natural log e cubed
- log subscript 4 baseline 64
- log 1,000