What is 6/5 ln| y/x-1|+ln|x| ?

The solution to 6/5 ln| y/x-1|+ln|x| is ln(| y/x-1|^{6/5}|x|)

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simplify 6/5 ln| y/x-1|+ln|x|

simplify

\frac{6}{5} ln \frac{y}{x} - 1 + ln ∣ x ∣

ln (\frac{y}{x} - 1^{\frac{6}{5}} ∣ x ∣)

Solution steps

\frac{6}{5} ln \frac{y}{x} - 1 + ln ∣ x ∣

Apply log rule:

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

\frac{6}{5} ln \frac{y}{x} - 1 = ln (\frac{y}{x} - 1^{\frac{6}{5}})

= ln (\frac{y}{x} - 1^{\frac{6}{5}}) + ln ∣ x ∣

Apply log rule:

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

ln (\frac{y}{x} - 1^{\frac{6}{5}}) + ln ∣ x ∣ = ln (∣ x ∣ \frac{y}{x} - 1^{\frac{6}{5}})

= ln (\frac{y}{x} - 1^{\frac{6}{5}} ∣ x ∣)

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What is 6/5 ln| y/x-1|+ln|x| ?
The solution to 6/5 ln| y/x-1|+ln|x| is ln(| y/x-1|^{6/5}|x|)