What is 4/17 ln(x)+12/17 ln(y) ?

The solution to 4/17 ln(x)+12/17 ln(y) is ln(x^{4/17}y^{12/17})

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simplify 4/17 ln(x)+12/17 ln(y)

simplify

\frac{4}{17} ln (x) + \frac{12}{17} ln (y)

ln (x^{\frac{4}{17}} y^{\frac{12}{17}})

Solution steps

\frac{4}{17} ln (x) + \frac{12}{17} ln (y)

Apply log rule:

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

\frac{4}{17} ln (x) = ln (x^{\frac{4}{17}})

= ln (x^{\frac{4}{17}}) + \frac{12}{17} ln (y)

Apply log rule:

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

\frac{12}{17} ln (y) = ln (y^{\frac{12}{17}})

= ln (x^{\frac{4}{17}}) + ln (y^{\frac{12}{17}})

Apply log rule:

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

ln (x^{\frac{4}{17}}) + ln (y^{\frac{12}{17}}) = ln (x^{\frac{4}{17}} y^{\frac{12}{17}})

= ln (x^{\frac{4}{17}} y^{\frac{12}{17}})

- 4 lo g_{6} (2 x)

lo g_{4} (2 x^{2} + x - 21) - lo g_{4} (x - 3)

lo g_{4} (x^{2} - 9) - 4 lo g_{4} (x + 3)

ln (x \cdot y)

- ln (\frac{1}{3})

What is 4/17 ln(x)+12/17 ln(y) ?
The solution to 4/17 ln(x)+12/17 ln(y) is ln(x^{4/17}y^{12/17})