simplify ln(a^4b^2)

Solution

simplify

ln (a^{4} b^{2})

4 ln (a) + 2 ln (b)

Solution steps

ln (a^{4} b^{2})

Apply log rule:

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

ln (a^{4} b^{2}) = ln (a^{4}) + ln (b^{2})

= ln (a^{4}) + ln (b^{2})

Apply log rule:

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

ln (a^{4}) = 4 ln (a)

= 4 ln (a) + ln (b^{2})

Apply log rule:

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

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

= 4 ln (a) + 2 ln (b)

ln (a^{2} - b^{2}) - 5 ln (c)

ln (\frac{25}{x})

ln (\frac{2}{3 \cdot e ^{x} + c})

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

lo g_{e} (x sin (x))