simplify ln(16θ^5)

Solution

simplify

ln (16 θ^{5})

4 ln (2) + 5 ln (θ)

Solution steps

ln (16 θ^{5})

Apply log rule:

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

ln (16 θ^{5}) = ln (16) + ln (θ^{5})

= ln (16) + ln (θ^{5})

Apply log rule:

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

ln (θ^{5}) = 5 ln (θ)

= ln (16) + 5 ln (θ)

ln (16) = 4 ln (2)

= 4 ln (2) + 5 ln (θ)

- ln (\frac{0.65}{0.8})

ln (\frac{1}{1 + e ( - ( b + a x + cy ) )})

ln (θ x^{- θ - 2})

3 ln (3 + i)

\frac{15}{9.5 \cdot 0.10305} \cdot ln (\frac{1}{1 - 0.8})