What is ln(x^8e^{-x(4.28*10^{-5})}) ?

The solution to ln(x^8e^{-x(4.28*10^{-5})}) is 8ln(x)-(4.28x)/(100000)

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simplify ln(x^8e^{-x(4.28*10^{-5})})

simplify

ln (x^{8} e^{- x (4.28 \cdot 1 0^{- 5})})

8 ln (x) - \frac{4.28 x}{100000}

Solution steps

ln (x^{8} e^{- x (4.28 \cdot 1 0^{- 5})})

Apply log rule:

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

ln (x^{8} e^{- x (4.28 \cdot 1 0^{- 5})}) = ln (x^{8}) + ln (e^{- x (4.28 \cdot 1 0^{- 5})})

= ln (x^{8}) + ln (e^{- (1 0^{- 5} \cdot 4.28) x})

Apply log rule:

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

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

= 8 ln (x) + ln (e^{- x \cdot 4.28 \cdot 1 0^{- 5}})

Apply log rule:

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

ln (e^{- x \cdot 4.28 \cdot 1 0^{- 5}}) = - x \cdot 4.28 \cdot 1 0^{- 5} ln (e)

= 8 ln (x) - x \cdot 4.28 \cdot 1 0^{- 5} ln (e)

x \cdot 4.28 \cdot 1 0^{- 5} ln (e) = 4.28 \cdot \frac{x}{100000}

= 8 ln (x) - 4.28 \cdot \frac{x}{100000}

Multiply

4.28 \cdot \frac{x}{100000} : \frac{4.28 x}{100000}

= 8 ln (x) - \frac{4.28 x}{100000}

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What is ln(x^8e^{-x(4.28*10^{-5})}) ?
The solution to ln(x^8e^{-x(4.28*10^{-5})}) is 8ln(x)-(4.28x)/(100000)