What is e^{-5x}+8ln(2z^4) ?

The solution to e^{-5x}+8ln(2z^4) is e^{-5x}+8ln(2)+32ln(z)

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simplify e^{-5x}+8ln(2z^4)

simplify

e^{- 5 x} + 8 ln (2 z^{4})

e^{- 5 x} + 8 ln (2) + 32 ln (z)

Solution steps

e^{- 5 x} + 8 ln (2 z^{4})

Apply log rule:

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

8 ln (2 z^{4}) = 8 ln (2) + 8 ln (z^{4})

= e^{- 5 x} + 8 ln (2) + 8 ln (z^{4})

Apply log rule:

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

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

= e^{- 5 x} + 8 ln (2) + 8 \cdot 4 ln (z)

Multiply the numbers:

8 \cdot 4 = 32

= e^{- 5 x} + 8 ln (2) + 32 ln (z)

ln (x^{n})

ln (5) + ln^{7} (- 3 ln^{2} (x))

ln (x) - 4 [ln (x - 6) + ln (x + 6)]

3 lo g_{b} (x) + 2 lo g_{b} (z)

lo g_{8} (\frac{1}{24})

What is e^{-5x}+8ln(2z^4) ?
The solution to e^{-5x}+8ln(2z^4) is e^{-5x}+8ln(2)+32ln(z)