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

The solution to e^{-ln(ln(x))-ln(x)} is 1/(xln(x))

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

simplify

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

\frac{1}{x ln ( x )}

Solution steps

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

Rewrite

- ln (ln (x)) - ln (x)

- (ln (ln (x)) + ln (x))

= e^{- (l n (l n (x)) + l n (x))}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (ln (x)) + ln (x) = ln (x ln (x))

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

Apply exponent rule:

a^{b c} = (a^{b})^{c}

= (e^{l n (l n (x) x)})^{- 1}

Apply log rule:

a^{l o g_{a} (b)} = b

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

= (ln (x) x)^{- 1}

Apply exponent rule:

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

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

\frac{1}{4} ln (6 b a^{2}) - ln (m) - \frac{1}{4} ln (5)

- lo g_{10} (2.19 \cdot 1 0^{- 6})

ln (1 - x) - ln (1 - y)

0 ln (\frac{500}{z})

\frac{ln ( 4.1 ) - ln ( 3.9 )}{2 \cdot 0.1}

What is e^{-ln(ln(x))-ln(x)} ?
The solution to e^{-ln(ln(x))-ln(x)} is 1/(xln(x))