What is simplify-4ln|x-1|+6ln|x|-1/x ?

The solution to simplify-4ln|x-1|+6ln|x|-1/x is ln((x^6)/((x-1)^4))-1/x

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simplify-4ln|x-1|+6ln|x|-1/x

simplify

- 4 ln ∣ x - 1 ∣ + 6 ln ∣ x ∣ - \frac{1}{x}

ln (\frac{x ^{6}}{( x - 1 ) ^{4}}) - \frac{1}{x}

Solution steps

- 4 ln ∣ x - 1 ∣ + 6 ln ∣ x ∣ - \frac{1}{x}

Apply log rule:

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

4 ln ∣ x - 1 ∣ = ln (∣ x - 1 ∣^{4})

= - ln (∣ x - 1 ∣^{4}) + 6 ln ∣ x ∣ - \frac{1}{x}

Apply log rule:

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

6 ln ∣ x ∣ = ln (∣ x ∣^{6})

= - ln (∣ x - 1 ∣^{4}) + ln (∣ x ∣^{6}) - \frac{1}{x}

Apply log rule:

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

ln (∣ x ∣^{6}) - ln (∣ x - 1 ∣^{4}) = ln (\frac{∣ x ∣ ^{6}}{∣ x - 1 ∣ ^{4}})

= ln (\frac{∣ x ∣ ^{6}}{∣ x - 1 ∣ ^{4}}) - \frac{1}{x}

Simplify

\frac{∣ x ∣ ^{6}}{∣ x - 1 ∣ ^{4}} : \frac{x ^{6}}{( x - 1 ) ^{4}}

= ln (\frac{x ^{6}}{( x - 1 ) ^{4}}) - \frac{1}{x}

4 + ln (4) - ln (\frac{10}{3})

lo g_{4} (\frac{x}{a ^{3}})

\frac{1}{4} ln (x^{12}) - 3 ln (2)

lo g_{10} (\frac{a ^{2}}{b ^{2} c})

lo g_{2} (5 \cdot 1 0^{9} \cdot 365 \cdot 24 \cdot 60 \cdot 60 \cdot 1 0^{6})

What is simplify-4ln|x-1|+6ln|x|-1/x ?
The solution to simplify-4ln|x-1|+6ln|x|-1/x is ln((x^6)/((x-1)^4))-1/x