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Popular >

simplify log_{e}(5e^{-2})

Solution

simplify

lo g_{e} (5 e^{- 2})

Solution

ln (5) - 2

+1

Decimal Notation

- 0.39056 \dots

Solution steps

lo g_{e} (5 e^{- 2})

Apply log rule:

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

lo g_{e} (5 e^{- 2}) = lo g_{e} (5) + lo g_{e} (e^{- 2})

= lo g_{e} (5) + lo g_{e} (e^{- 2})

Apply log rule:

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

lo g_{e} (e^{- 2}) = - 2 lo g_{e} (e)

= lo g_{e} (5) - 2 lo g_{e} (e)

lo g_{e} (5) = ln (5)

2 lo g_{e} (e) = 2

= ln (5) - 2

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Frequently Asked Questions (FAQ)

What is log_{e}(5e^{-2}) ?
The solution to log_{e}(5e^{-2}) is ln(5)-2