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

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

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

simplify

- 2 ln ∣ ln (x) ∣ - ln (x)

- ln (x ln^{2} (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 (x) ∣^{2})

= - ln (∣ ln (x) ∣^{2}) - ln (x)

Rewrite

- ln (∣ ln (x) ∣^{2}) - ln (x)

- (ln (∣ ln (x) ∣^{2}) + ln (x))

= - (ln (∣ ln (x) ∣^{2}) + ln (x))

Apply log rule:

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

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

= - ln (x ∣ ln (x) ∣^{2})

∣ ln (x) ∣^{2} = ln^{2} (x)

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

10 \cdot ln (0.5 \cdot X)

6 lo g_{9} (x) - 3 lo g_{9} (y)

- lo g_{10} (8.7 \cdot 1 0^{- 9})

\frac{1}{2} lo g_{10} (x) + lo g_{10} (y)

0.33 \cdot lo g_{10} (0.33) + 0.67 \cdot lo g_{10} (0.67)

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