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}

ln (\frac{1}{x + 2})

- lo g_{10} (7 \cdot 1 0^{- 5})

ln (\frac{20}{17})

lo g_{3} (y) + lo g_{3} (y + 3)

lo g_{5} (35 \cdot 15)

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