What is ae^{-ln(a)}(1-ln(a)) ?

The solution to ae^{-ln(a)}(1-ln(a)) is -ln(a)+1

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simplify ae^{-ln(a)}(1-ln(a))

simplify

a e^{- l n (a)} (1 - ln (a))

- ln (a) + 1

Solution steps

a e^{- l n (a)} (1 - ln (a))

Apply exponent rule:

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

= a \frac{1}{e ^{l n (a)}} (- ln (a) + 1)

\frac{1}{e ^{l n (a)}} = \frac{1}{a}

= a \frac{1}{a} (- ln (a) + 1)

Multiply fractions:

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

= \frac{1 \cdot a ( 1 - ln ( a ) )}{a}

Cancel the common factor:

a

= 1 \cdot (1 - ln (a))

Refine

= 1 - ln (a)

\frac{4}{3} π (1 \cdot 1 0^{- 13})

h (x) 1. 4^{- x^{2}}

5 e^{- 10}

32 x^{2} y^{2} x y

8.97 \cdot 1 0^{- 7}