simplify ln(5x^3)

Solution

simplify

ln (5 x^{3})

ln (5) + 3 ln (x)

Solution steps

ln (5 x^{3})

Apply log rule:

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

ln (5 x^{3}) = ln (5) + ln (x^{3})

= ln (5) + ln (x^{3})

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= ln (5) + 3 ln (x)

ln (2) - ln (6)

lo g_{4} (\frac{64}{x + 2})

- (\frac{1}{3} lo g_{2} (\frac{1}{3}) + \frac{2}{3} lo g_{2} (\frac{2}{3}))

\frac{2 ln ( 2 )}{ln ( 5 ) - 2 ln ( 2 )}

lo g_{10} (\frac{x ^{6} y}{z})