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Popular >

simplify ln(sqrt(e^u))

Solution

simplify

ln (e^{u})

Solution

\frac{u}{2}

Solution steps

ln (e^{u})

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

Apply log rule:

lo g_{a} (a) = 1

= \frac{1}{2} u

Simplify

= \frac{u}{2}

Popular Examples

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\frac{4}{x - 1} + \frac{2}{3 x}

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\frac{4 h}{h}

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3 x^{2} 12 x

simplify sqrt(1^2+8^2)simplify

1^{2} + 8^{2}

33/4 \div 4 1/2

\frac{33}{4} \div 4 \frac{1}{2}

Frequently Asked Questions (FAQ)

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