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

The solution to 6ln(x)-1/5 ln(y) is ln((x^6y^{4/5})/y)

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

simplify

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

ln (\frac{x ^{6} y ^{\frac{4}{5}}}{y})

Solution steps

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

Apply log rule:

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

6 ln (x) = ln (x^{6})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{6}}{y ^{\frac{1}{5}}} : \frac{x ^{6} y ^{\frac{4}{5}}}{y}

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

3^{\frac{l n ( \frac{4}{l n ( 3 )} )}{l n ( 3 )}} ln (3)

lo g_{8} (7 x)

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ln (2.5 \cdot 1 0^{- 3}) + (\frac{130000}{8.314 \cdot 473})

ln (\frac{1}{2} x + 4 + x^{2})

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