What is ln((3e^{-n^3+nx})/x) ?

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

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simplify ln((3e^{-n^3+nx})/x)

simplify

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

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

Solution steps

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

Apply log rule:

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

ln (\frac{3 e ^{- n^{3} + n x}}{x}) = ln (3 e^{- n^{3} + n x}) - ln (x)

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

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

Remove parentheses:

(- a) = - a

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

ln ∣ x ∣ - ln x^{2} + 1

lo g_{10} (\frac{( 2 sin ( x ) )}{sin ( 2 x )})

\frac{1}{2} ln (4 + y^{2}) - \frac{1}{2} ln (1 - y^{2})

20 \cdot lo g_{10} (\frac{4 \cdot π \cdot 30}{\frac{300}{175}})

\frac{100}{7} ln (5)

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