What is simplify-ln(2.05e^{-4}) ?

The solution to simplify-ln(2.05e^{-4}) is -ln(2.05)+4

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simplify-ln(2.05e^{-4})

simplify

- ln (2.05 e^{- 4})

- ln (2.05) + 4

Decimal Notation

3.28216 \dots

Solution steps

- ln (2.05 e^{- 4})

Apply log rule:

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

ln (2.05 e^{- 4}) = ln (2.05) + ln (e^{- 4})

= - (ln (2.05) + ln (e^{- 4}))

Apply log rule:

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

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

= - (ln (2.05) - 4 ln (e))

4 ln (e) = 4

= - (ln (2.05) - 4)

Distribute parentheses

= - (ln (2.05)) - (- 4)

Apply minus-plus rules

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

= - ln (2.05) + 4

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What is simplify-ln(2.05e^{-4}) ?
The solution to simplify-ln(2.05e^{-4}) is -ln(2.05)+4