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Popular >

simplify ln(sqrt(e^x))

Solution

simplify

ln (e^{x})

Solution

\frac{x}{2}

Solution steps

ln (e^{x})

Rewrite as

= ln ((e^{x})^{\frac{1}{2}})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{2} ln (e^{x})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x),

assuming

x \geq 0

= \frac{1}{2} ln (e) x

Apply log rule:

lo g_{a} (a) = 1

= \frac{1}{2} x

Simplify

= \frac{x}{2}

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Frequently Asked Questions (FAQ)

What is ln(sqrt(e^x)) ?
The solution to ln(sqrt(e^x)) is x/2