What is simplify-ln(4e^{-8}) ?

The solution to simplify-ln(4e^{-8}) is -2ln(2)+8

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simplify-ln(4e^{-8})

simplify

- ln (4 e^{- 8})

- 2 ln (2) + 8

Decimal Notation

6.61370 \dots

Solution steps

- ln (4 e^{- 8})

Apply log rule:

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

ln (4 e^{- 8}) = ln (4) + ln (e^{- 8})

= - (ln (4) + ln (e^{- 8}))

Apply log rule:

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

ln (e^{- 8}) = - 8 ln (e)

= - (ln (4) - 8 ln (e))

8 ln (e) = 8

= - (ln (4) - 8)

ln (4) = 2 ln (2)

= - (2 ln (2) - 8)

Distribute parentheses

= - (2 ln (2)) - (- 8)

Apply minus-plus rules

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

= - 2 ln (2) + 8

ln (\frac{1}{x + h} + 1) - ln (\frac{1}{x} + 1)

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

- 1.44 - 5 lo g_{10} (\frac{2.6}{10})

ln (4 x) + ln (x^{2})

ln (8 x^{2}) - 2 ln (2 x)

What is simplify-ln(4e^{-8}) ?
The solution to simplify-ln(4e^{-8}) is -2ln(2)+8