What is e^{-4z}+6ln(3z^5) ?

The solution to e^{-4z}+6ln(3z^5) is e^{-4z}+6ln(3)+30ln(z)

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simplify e^{-4z}+6ln(3z^5)

simplify

e^{- 4 z} + 6 ln (3 z^{5})

e^{- 4 z} + 6 ln (3) + 30 ln (z)

Solution steps

e^{- 4 z} + 6 ln (3 z^{5})

Apply log rule:

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

6 ln (3 z^{5}) = 6 ln (3) + 6 ln (z^{5})

= e^{- 4 z} + 6 ln (3) + 6 ln (z^{5})

Apply log rule:

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

ln (z^{5}) = 5 ln (z)

= e^{- 4 z} + 6 ln (3) + 6 \cdot 5 ln (z)

Multiply the numbers:

6 \cdot 5 = 30

= e^{- 4 z} + 6 ln (3) + 30 ln (z)

\frac{9}{5} ln (4) - \frac{9}{5} ln (3)

ln (\frac{828}{613.1})

lo g_{2} (\frac{( x y ) ^{4}}{z ^{2}})

ln (\frac{1806}{1400})

ln (- in f ini t y)

What is e^{-4z}+6ln(3z^5) ?
The solution to e^{-4z}+6ln(3z^5) is e^{-4z}+6ln(3)+30ln(z)