Question

simplify each expression.
\\(\ln e^3 = \\)
\\(\ln e^{2y} = \\)
\\(e^{\ln 1} = \\)
\\(e^{\ln 5x} = \\)

Explanation:

Simplify the first expression

Using the Inverse Properties of Logarithms knowledge point

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

Simplify the second expression

Using the Inverse Properties of Logarithms knowledge point

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

Simplify the third expression

Using the Inverse Properties of Logarithms knowledge point

$$ e^{\ln(1)} = 1 $$

Simplify the fourth expression

Using the Inverse Properties of Logarithms knowledge point

$$ e^{\ln(5x)} = 5x $$

Answer:

Question 1

\(\ln e^3 =\) <blank>3</blank>

Question 2

\(\ln e^{2y} =\) <blank>\(2y\)</blank>

Question 3

\(e^{\ln 1} =\) <blank>1</blank>

Question 4

\(e^{\ln 5x} =\) <blank>\(5x\)</blank>