What is ln(x^2e^{x/y dy}) ?

The solution to ln(x^2e^{x/y dy}) is 2ln(x)+xd

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simplify ln(x^2e^{x/y dy})

simplify

ln (x^{2} e^{\frac{x}{y} d y})

2 ln (x) + x d

Solution steps

ln (x^{2} e^{\frac{x}{y} d y})

Apply log rule:

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

ln (x^{2} e^{\frac{x}{y} d y}) = ln (x^{2}) + ln (e^{\frac{x}{y} d y})

= ln (x^{2}) + ln (e^{\frac{x}{y} y d})

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

= 2 ln (x) + ln (e^{\frac{x}{y} d y})

Apply log rule:

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

ln (e^{\frac{x}{y} d y}) = \frac{x}{y} d y ln (e)

= 2 ln (x) + \frac{x}{y} d y ln (e)

\frac{x}{y} d y ln (e) = x d

= 2 ln (x) + x d

lo g_{b} (s^{19})

ln (x) + 2 ln (p) - ln (8 p^{2} - 1)

ln (a + b) + 5 ln (a - b) - 5 ln (c)

ln (\frac{x + 1}{1 - x})

- ln (8) + ln (6) + ln (3) - ln (1)