What is ln(ae^{a(-5)}(-5)) ?

The solution to ln(ae^{a(-5)}(-5)) is ln(a)-5a+ln(-5)

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simplify ln(ae^{a(-5)}(-5))

simplify

ln (a e^{a (- 5)} (- 5))

ln (a) - 5 a + ln (- 5)

Solution steps

ln (a e^{a (- 5)} (- 5))

Apply log rule:

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

ln (a e^{a (- 5)} (- 5)) = ln (a) + ln (e^{a (- 5)}) + ln (- 5)

= ln (a) + ln (e^{(- 5) a}) + ln (- 5)

Apply log rule:

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

ln (e^{a (- 5)}) = a (- 5) ln (e)

= ln (a) + a (- 5) ln (e) + ln (- 5)

Remove parentheses:

(- a) = - a

= ln (a) - a \cdot 5 ln (e) + ln (- 5)

a \cdot 5 ln (e) = 5 a

= ln (a) - 5 a + ln (- 5)

x \to \infty lim (ln (\frac{1}{x}))

ln (y^{s i n (x)} \cdot y)

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

(\frac{1}{2}) lo g_{b} (a) - 5 lo g_{b} (c)

ln (\frac{100 + 0.11}{0.11})

What is ln(ae^{a(-5)}(-5)) ?
The solution to ln(ae^{a(-5)}(-5)) is ln(a)-5a+ln(-5)