simplify ln(6x^8)

Solution

simplify

ln (6 x^{8})

ln (6) + 8 ln (x)

Solution steps

ln (6 x^{8})

Apply log rule:

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

ln (6 x^{8}) = ln (6) + ln (x^{8})

= ln (6) + ln (x^{8})

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= ln (6) + 8 ln (x)

\frac{1}{3} (2 ln (x) + ln (y) - 2 ln (z))

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

lo g_{10} (z^{4} y)

20 ln (\frac{1400}{1400 + 100 ( 10 )}) + 9.8 (10)

lo g_{x} (- 2 lo g_{y} (+ 5 lo g_{z} (x)))