What is e^{x+ln(x)}+ln(1/(x^3)) ?

The solution to e^{x+ln(x)}+ln(1/(x^3)) is e^{x+ln(x)}++ln(1)-3ln(x)

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simplify e^{x+ln(x)}+ln(1/(x^3))

simplify

e^{x + l n (x)} + ln (\frac{1}{x ^{3}})

e^{x + l n (x)} + + ln (1) - 3 ln (x)

Solution steps

e^{x + l n (x)} + ln (\frac{1}{x ^{3}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{x ^{3}}) = ln (1) - ln (x^{3})

= e^{x + l n (x)} + + ln (1) - ln (x^{3})

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= e^{x + l n (x)} + + ln (1) - 3 ln (x)

lo g_{5} (7 \cdot 11)

- 12 (\frac{1}{2} ln ∣ 8 x - 8 ∣ - \frac{1}{2} ln ∣ 8 x - 10 ∣) + C

- \frac{1}{40} ln (\frac{1}{10})

\frac{1}{2} lo g_{5} (12)

- lo g_{10} (6.66 \cdot 1 0^{- 5})

What is e^{x+ln(x)}+ln(1/(x^3)) ?
The solution to e^{x+ln(x)}+ln(1/(x^3)) is e^{x+ln(x)}++ln(1)-3ln(x)