simplify 4ln(2z^2)

Solution

simplify

4 ln (2 z^{2})

4 ln (2) + 8 ln (z)

Solution steps

4 ln (2 z^{2})

Apply log rule:

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

4 ln (2 z^{2}) = 4 ln (2) + 4 ln (z^{2})

= 4 ln (2) + 4 ln (z^{2})

Apply log rule:

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

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

= 4 ln (2) + 4 \cdot 2 ln (z)

Multiply the numbers:

4 \cdot 2 = 8

= 4 ln (2) + 8 ln (z)

(1.0299) \cdot ln (\frac{80}{250}) - (0.41195) ln (\frac{550}{240})

ln (\frac{100 + 150}{150})

182000 \cdot [ln (0.5) - ln (1.3)]

ln (\frac{- θ - 1}{θ - 1}) \cdot (- 1)

ln (y - 1) - ln (y + 1)