What is log_{10}((x^3e^{-x})/(4.408)) ?

The solution to log_{10}((x^3e^{-x})/(4.408)) is 3log_{10}(x)-xlog_{10}(e)-log_{10}(4.408)

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simplify log_{10}((x^3e^{-x})/(4.408))

simplify

lo g_{10} (\frac{x ^{3} e ^{- x}}{4.408})

3 lo g_{10} (x) - x lo g_{10} (e) - lo g_{10} (4.408)

Solution steps

lo g_{10} (\frac{x ^{3} e ^{- x}}{4.408})

Apply log rule:

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

lo g_{10} (\frac{x ^{3} e ^{- x}}{4.408}) = lo g_{10} (x^{3} e^{- x}) - lo g_{10} (4.408)

= lo g_{10} (e^{- x} x^{3}) - lo g_{10} (4.408)

Apply log rule:

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

lo g_{10} (x^{3} e^{- x}) = lo g_{10} (x^{3}) + lo g_{10} (e^{- x})

= lo g_{10} (x^{3}) + lo g_{10} (e^{- x}) - lo g_{10} (4.408)

Apply log rule:

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

lo g_{10} (x^{3}) = 3 lo g_{10} (x)

= 3 lo g_{10} (x) + lo g_{10} (e^{- x}) - lo g_{10} (4.408)

Apply log rule:

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

lo g_{10} (e^{- x}) = - x lo g_{10} (e)

= 3 lo g_{10} (x) - x lo g_{10} (e) - lo g_{10} (4.408)

ln (3) + ln (2) + ln (2)

ln (\frac{e ^{6}}{7})

lo g_{5} (3 x) \cdot ln (5)

e^{\frac{1}{4} (l n (2 x + 1) - l n (2 x - 1))}

\frac{ln ( 2.99 ) - ln ( 3 )}{( 2.99 ) - 3}

What is log_{10}((x^3e^{-x})/(4.408)) ?
The solution to log_{10}((x^3e^{-x})/(4.408)) is 3log_{10}(x)-xlog_{10}(e)-log_{10}(4.408)