simplify ln(8x^3)

Solution

simplify

ln (8 x^{3})

3 ln (2) + 3 ln (x)

Solution steps

ln (8 x^{3})

Apply log rule:

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

ln (8 x^{3}) = ln (8) + ln (x^{3})

= ln (8) + ln (x^{3})

Apply log rule:

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

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

= ln (8) + 3 ln (x)

ln (8) = 3 ln (2)

= 3 ln (2) + 3 ln (x)

lo g_{2} (x) - lo g_{2} (x^{7})

- \frac{1}{6} lo g_{2} (\frac{1}{6}) - \frac{5}{6} lo g_{2} (\frac{5}{6})

- lo g_{10} (7.4 \cdot 1 0^{- 4})

ln ((x y)^{3})

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