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Popular >

simplify ln(8*e^{-8x})

Solution

simplify

ln (8 \cdot e^{- 8 x})

Solution

3 ln (2) - 8 x

Solution steps

ln (8 e^{- 8 x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (8) - 8 x ln (e)

8 x ln (e) = 8 x

= ln (8) - 8 x

ln (8) = 3 ln (2)

= 3 ln (2) - 8 x

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Frequently Asked Questions (FAQ)

What is ln(8*e^{-8x}) ?
The solution to ln(8*e^{-8x}) is 3ln(2)-8x