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Popular >

simplify ln(sqrt((e^u+3)-3))

Solution

simplify

ln ((e^{u} + 3) - 3)

Solution

\frac{u}{2}

Solution steps

ln ((e^{u} + 3) - 3)

Remove parentheses:

(a) = a

= ln (e^{u} + 3 - 3)

3 - 3 = 0

= 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}

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Frequently Asked Questions (FAQ)

What is ln(sqrt((e^u+3)-3)) ?
The solution to ln(sqrt((e^u+3)-3)) is u/2