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Popular >

simplify ln(5e^{-2x})

Solution

simplify

ln (5 e^{- 2 x})

Solution

ln (5) - 2 x

Solution steps

ln (5 e^{- 2 x})

Apply log rule:

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

ln (5 e^{- 2 x}) = ln (5) + ln (e^{- 2 x})

= ln (5) + ln (e^{- 2 x})

Apply log rule:

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

ln (e^{- 2 x}) = - 2 x ln (e)

= ln (5) - 2 x ln (e)

2 x ln (e) = 2 x

= ln (5) - 2 x

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Frequently Asked Questions (FAQ)

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