What is ln(-10e^{-(2sqrt(10))/5 x}) ?

The solution to ln(-10e^{-(2sqrt(10))/5 x}) is ln(10)-(2sqrt(10)x)/5

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simplify ln(-10e^{-(2sqrt(10))/5 x})

simplify

ln (- 10 e^{- \frac{2 10}{5} x})

ln (10) - \frac{2 10 x}{5}

Solution steps

ln (- 10 e^{- \frac{2 10}{5} x})

Apply log rule:

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

ln (- 10 e^{- \frac{2 10}{5} x}) = ln (10) + ln (e^{- \frac{2 10}{5} x})

= ln (10) + ln (e^{- \frac{2 10}{5} x})

Apply log rule:

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

ln (e^{- \frac{2 10}{5} x}) = - \frac{2 10}{5} x ln (e)

= ln (10) - \frac{2 10}{5} x ln (e)

\frac{2 10}{5} x ln (e) = \frac{2 10 x}{5}

= ln (10) - \frac{2 10 x}{5}

lo g_{12} (\frac{12 13}{11 n})

- \frac{1}{24} ln (\frac{15}{20})

ln (u) - ln (x)

- 0.05 lo g_{2} (0.05) - 0.95 lo g_{2} (0.95)

ln (\frac{x x + 1}{2 e ^{4}})

What is ln(-10e^{-(2sqrt(10))/5 x}) ?
The solution to ln(-10e^{-(2sqrt(10))/5 x}) is ln(10)-(2sqrt(10)x)/5