What is simplify-2ln(ln(x))-ln(x) ?

The solution to simplify-2ln(ln(x))-ln(x) is -ln(ln^2(x)x)

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simplify-2ln(ln(x))-ln(x)

simplify

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

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

Solution steps

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

Apply log rule:

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

2 ln (ln (x)) = ln (ln^{2} (x))

= - ln (ln^{2} (x)) - ln (x)

Rewrite

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

- (ln (ln^{2} (x)) + ln (x))

= - (ln (ln^{2} (x)) + ln (x))

Apply log rule:

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

ln (ln^{2} (x)) + ln (x) = ln (x ln^{2} (x))

= - ln (ln^{2} (x) x)

ln (\frac{2}{3}) + ln (3)

ln (11) - ln (50) - \frac{12 π}{5}

ln (\frac{6 y - 5}{y})

- 5137.521 + 1239.973 ln (\frac{1938}{30})

What is simplify-2ln(ln(x))-ln(x) ?
The solution to simplify-2ln(ln(x))-ln(x) is -ln(ln^2(x)x)