Question

simplify each expression.

\\(\ln e^{3} = \\)

\\(\ln e^{2y} = \\)

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Simplify the first expression

The natural logarithm \(\ln(x)\) is the logarithm with base \(e\).

Using the inverse property of logarithms, \(\ln(e^x) = x\):

$$ \ln(e^3) = 3 $$

Step 2: Simplify the second expression

Using the same inverse property \(\ln(e^x) = x\):

$$ \ln(e^{2y}) = 2y $$

Answer:

• \(\ln(e^3) = 3\)
• \(\ln(e^{2y}) = 2y\)