What is ln(y/(x^{2n)}*e^{(-m)/x}) ?

The solution to ln(y/(x^{2n)}*e^{(-m)/x}) is ln(y)-2nln(x)-m/x

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simplify ln(y/(x^{2n)}*e^{(-m)/x})

simplify

ln (\frac{y}{x ^{2 n}} \cdot e^{\frac{- m}{x}})

ln (y) - 2 n ln (x) - \frac{m}{x}

Solution steps

ln (\frac{y}{x ^{2 n}} e^{\frac{- m}{x}})

Apply log rule:

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

ln (\frac{y}{x ^{2 n}} e^{\frac{- m}{x}}) = ln (\frac{y}{x ^{2 n}}) + ln (e^{\frac{- m}{x}})

= ln (\frac{y}{x ^{2 n}}) + ln (e^{\frac{- m}{x}})

Apply log rule:

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

ln (e^{\frac{- m}{x}}) = \frac{- m}{x} ln (e)

= ln (\frac{y}{x ^{2 n}}) + \frac{- m}{x} ln (e)

Apply log rule:

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

ln (\frac{y}{x ^{2 n}}) = ln (y) - ln (x^{2 n})

= ln (y) - ln (x^{2 n}) + ln (e) \frac{- m}{x}

Apply log rule:

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

ln (x^{2 n}) = 2 n ln (x)

= ln (y) - 2 n ln (x) + \frac{- m}{x} ln (e)

\frac{- m}{x} ln (e) = - \frac{m}{x}

= ln (y) - 2 n ln (x) - \frac{m}{x}

ln (- 2 y d y)

ln (d + w) - ln (d)

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

10 lo g_{10} (\frac{50 \cdot 1 0 ^{- 3}}{1 \cdot 1 0 ^{- 6}})

4 ln (x) + ln (y)

What is ln(y/(x^{2n)}*e^{(-m)/x}) ?
The solution to ln(y/(x^{2n)}*e^{(-m)/x}) is ln(y)-2nln(x)-m/x