What is log_{e}((x^3-3x+9)/(x^3)) ?

The solution to log_{e}((x^3-3x+9)/(x^3)) is ln(x^3-3x+9)-3ln(x)

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simplify log_{e}((x^3-3x+9)/(x^3))

simplify

lo g_{e} (\frac{x ^{3} - 3 x + 9}{x ^{3}})

ln (x^{3} - 3 x + 9) - 3 ln (x)

Solution steps

lo g_{e} (\frac{x ^{3} - 3 x + 9}{x ^{3}})

Apply log rule:

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

lo g_{e} (\frac{x ^{3} - 3 x + 9}{x ^{3}}) = lo g_{e} (x^{3} - 3 x + 9) - lo g_{e} (x^{3})

= lo g_{e} (x^{3} - 3 x + 9) - lo g_{e} (x^{3})

Apply log rule:

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

lo g_{e} (x^{3}) = 3 lo g_{e} (x)

= lo g_{e} (x^{3} - 3 x + 9) - 3 lo g_{e} (x)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (x^{3} - 3 x + 9) - 3 lo g_{e} (x)

Simplify

lo g_{e} (x) : ln (x)

= ln (x^{3} - 3 x + 9) - 3 ln (x)

- lo g_{10} (4.29 \cdot 1 0^{- 6})

- ln (\frac{16}{15})

lo g_{4} (x) + 5 lo g_{4} (y)

lo g_{2} (55) \cdot \frac{3}{2}

lo g_{10} (\frac{0.651}{0.349}) - 0.5 \cdot (- 0.30134)

What is log_{e}((x^3-3x+9)/(x^3)) ?
The solution to log_{e}((x^3-3x+9)/(x^3)) is ln(x^3-3x+9)-3ln(x)