What is 6/5 ln(y/x+4)-1/5 ln(y/x-1)+ln(x) ?

The solution to 6/5 ln(y/x+4)-1/5 ln(y/x-1)+ln(x) is ln(\sqrt[5]{((y+4x)^6)/(y-x)})

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simplify 6/5 ln(y/x+4)-1/5 ln(y/x-1)+ln(x)

simplify

\frac{6}{5} ln (\frac{y}{x} + 4) - \frac{1}{5} ln (\frac{y}{x} - 1) + ln (x)

Solution steps

\frac{6}{5} ln (\frac{y}{x} + 4) - \frac{1}{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} + 4) = ln ((\frac{y}{x} + 4)^{\frac{6}{5}})

= ln ((\frac{y}{x} + 4)^{\frac{6}{5}}) - \frac{1}{5} ln (\frac{y}{x} - 1) + ln (x)

Apply log rule:

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

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

= ln ((\frac{y}{x} + 4)^{\frac{6}{5}}) - ln ((\frac{y}{x} - 1)^{\frac{1}{5}}) + ln (x)

Apply log rule:

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

ln ((\frac{y}{x} + 4)^{\frac{6}{5}}) - ln ((\frac{y}{x} - 1)^{\frac{1}{5}}) = ln \frac{( \frac{y}{x} + 4 ) ^{\frac{6}{5}}}{( \frac{y}{x} - 1 ) ^{\frac{1}{5}}}

= ln \frac{( \frac{y}{x} + 4 ) ^{\frac{6}{5}}}{( \frac{y}{x} - 1 ) ^{\frac{1}{5}}} + ln (x)

Simplify

\frac{( \frac{y}{x} + 4 ) ^{\frac{6}{5}}}{( \frac{y}{x} - 1 ) ^{\frac{1}{5}}} : \frac{( y + 4 x ) ^{\frac{6}{5}} ( y - x ) ^{\frac{4}{5}}}{y x - x ^{2}}

= ln (\frac{( y + 4 x ) ^{\frac{6}{5}} ( y - x ) ^{\frac{4}{5}}}{y x - x ^{2}}) + ln (x)

Apply log rule:

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

ln (\frac{( y + 4 x ) ^{\frac{6}{5}} ( y - x ) ^{\frac{4}{5}}}{y x - x ^{2}}) + ln (x) = ln (\frac{( y - x ) ^{\frac{4}{5}} ( y + 4 x ) ^{\frac{6}{5}}}{- x ^{2} + y x} x)

= ln (\frac{( y + 4 x ) ^{\frac{6}{5}} ( y - x ) ^{\frac{4}{5}}}{- x ^{2} + y x} x)

Simplify

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

ln (\frac{1}{0.15})

ln (\frac{84}{92})

\frac{1}{0.26 - 0.17} ln (\frac{0.26}{0.17})

\frac{1}{5} ln (\frac{1}{5 - 0.8 Q})

What is 6/5 ln(y/x+4)-1/5 ln(y/x-1)+ln(x) ?
The solution to 6/5 ln(y/x+4)-1/5 ln(y/x-1)+ln(x) is ln(\sqrt[5]{((y+4x)^6)/(y-x)})