What is x/(ln(x))(ln(x)-ln(x^3)) ?

The solution to x/(ln(x))(ln(x)-ln(x^3)) is -(xln(x^2))/(ln(x))

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simplify x/(ln(x))(ln(x)-ln(x^3))

simplify

\frac{x}{ln ( x )} (ln (x) - ln (x^{3}))

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

Solution steps

\frac{x}{ln ( x )} (ln (x) - ln (x^{3}))

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x) - ln (x^{3}) = ln (\frac{x}{x ^{3}})

= \frac{x}{ln ( x )} ln (\frac{x}{x ^{3}})

Cancel the common factor:

x

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

Multiply fractions:

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

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

Simplify

ln (\frac{1}{x ^{2}}) : - ln (x^{2})

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

Remove parentheses:

(- a) = - a

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

Apply the fraction rule:

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

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

- lo g_{10} (2.8 \cdot 1 0^{- 4})

5 lo g_{10} (x) + 3 lo g_{10} (y)

lo g_{3} (x) + 4 lo g_{3} (y)

\frac{1}{3} ln ∣ y - 1 ∣ - \frac{1}{3} ln ∣ y + 2 ∣

ln (20) + 2 ln (\frac{1}{2}) + \frac{1}{3} ln (27)

What is x/(ln(x))(ln(x)-ln(x^3)) ?
The solution to x/(ln(x))(ln(x)-ln(x^3)) is -(xln(x^2))/(ln(x))