What is e^{2ln(x)}*ln(x)*x^{-2} ?

The solution to e^{2ln(x)}*ln(x)*x^{-2} is ln(x)

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simplify e^{2ln(x)}ln(x)x^{-2}

simplify

e^{2 l n (x)} \cdot ln (x) \cdot x^{- 2}

ln (x)

Solution steps

e^{2 l n (x)} ln (x) x^{- 2}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

e^{2 l n (x)} = x^{2}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

x^{2}

= 1 \cdot ln (x)

Multiply:

1 \cdot ln (x) = ln (x)

= ln (x)

\frac{2}{2 π}

(\frac{1}{πk t})^{\frac{3}{2}} k t

x^{2} (5 - x)^{2}

(2 x^{2}) (7 x^{4})

8 \cdot e^{- 5}

What is e^{2ln(x)}*ln(x)*x^{-2} ?
The solution to e^{2ln(x)}*ln(x)*x^{-2} is ln(x)