What is simplify-ln((10*e^{-x}+40-4)/(10)) ?

The solution to simplify-ln((10*e^{-x}+40-4)/(10)) is -ln(10e^{-x}+36)+ln(10)

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simplify-ln((10*e^{-x}+40-4)/(10))

simplify

- ln (\frac{10 \cdot e ^{- x} + 40 - 4}{10})

- ln (10 e^{- x} + 36) + ln (10)

Solution steps

- ln (\frac{10 e ^{- x} + 40 - 4}{10})

Apply log rule:

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

ln (\frac{10 e ^{- x} + 40 - 4}{10}) = ln (10 e^{- x} + 40 - 4) - ln (10)

= - (ln (10 e^{- x} + 40 - 4) - ln (10))

Add/Subtract the numbers:

40 - 4 = 36

= - (ln (10 e^{- x} + 36) - ln (10))

Distribute parentheses

= - (ln (10 e^{- x} + 36)) - (- ln (10))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - ln (10 e^{- x} + 36) + ln (10)

ln (\frac{t}{x})

- lo g_{10} (3.16 \cdot 1 0^{- 9})

ln (\frac{l}{x !})

lo g_{10} (5^{3 - x})

lo g_{3} (6 x^{2})

What is simplify-ln((10*e^{-x}+40-4)/(10)) ?
The solution to simplify-ln((10*e^{-x}+40-4)/(10)) is -ln(10e^{-x}+36)+ln(10)