simplify ln(xy^x)

Solution

simplify

ln (x y^{x})

ln (x) + x ln (y)

Solution steps

ln (x y^{x})

Apply log rule:

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

ln (x y^{x}) = ln (x) + ln (y^{x})

= ln (x) + ln (y^{x})

Apply log rule:

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

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

= ln (x) + x ln (y)

lo g_{b} (\frac{25}{x + 7})

ln ((4 x^{2} + 3) (2 x - 1))

ln (1) - \frac{1}{8} (ln (\frac{17}{4} + 2) + ln (\frac{17}{4}))

ln (x + 6) + ln (x + 1)

ln (1 + 3 x) - ln (1 - x)