simplify ln(11x^4y)

Solution

simplify

ln (11 x^{4} y)

ln (11) + 4 ln (x) + ln (y)

Solution steps

ln (11 x^{4} y)

Apply log rule:

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

ln (11 x^{4} y) = ln (11) + ln (x^{4}) + ln (y)

= ln (11) + ln (x^{4}) + ln (y)

Apply log rule:

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

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

= ln (11) + 4 ln (x) + ln (y)

ln (- 2) - ln (- 1)

ln (a) + ln (c)

ln (9 x^{0.3})

- \frac{1}{2} ln (\frac{3}{16}) + ln (\frac{1}{2}) - \frac{4}{3}

10 lo g_{10} (\frac{1}{86400} 1 0^{\frac{15}{10}})