What is ln(x^{2/5}y^{4/3}) ?

The solution to ln(x^{2/5}y^{4/3}) is 2/5 ln(x)+4/3 ln(y)

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simplify ln(x^{2/5}y^{4/3})

simplify

ln (x^{\frac{2}{5}} y^{\frac{4}{3}})

\frac{2}{5} ln (x) + \frac{4}{3} ln (y)

Solution steps

ln (x^{\frac{2}{5}} y^{\frac{4}{3}})

Apply log rule:

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

ln (x^{\frac{2}{5}} y^{\frac{4}{3}}) = ln (x^{\frac{2}{5}}) + ln (y^{\frac{4}{3}})

= ln (x^{\frac{2}{5}}) + ln (y^{\frac{4}{3}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{\frac{2}{5}}) = \frac{2}{5} ln (x)

= \frac{2}{5} ln (x) + ln (y^{\frac{4}{3}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (y^{\frac{4}{3}}) = \frac{4}{3} ln (y)

= \frac{2}{5} ln (x) + \frac{4}{3} ln (y)

ln (\frac{30}{15})

- 26.8 - 5 lo g_{10} (\frac{4.848 \cdot 1 0 ^{- 6}}{10})

\frac{2}{3} lo g_{2} (15)

lo g_{10} (5 \cdot e^{9})

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

What is ln(x^{2/5}y^{4/3}) ?
The solution to ln(x^{2/5}y^{4/3}) is 2/5 ln(x)+4/3 ln(y)