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Popular >

simplify ln(4e^{-t/c})

Solution

simplify

ln (4 e^{- \frac{t}{c}})

Solution

2 ln (2) - \frac{t}{c}

Solution steps

ln (4 e^{- \frac{t}{c}})

Apply log rule:

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

ln (4 e^{- \frac{t}{c}}) = ln (4) + ln (e^{- \frac{t}{c}})

= ln (4) + ln (e^{- \frac{t}{c}})

Apply log rule:

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

ln (e^{- \frac{t}{c}}) = - \frac{t}{c} ln (e)

= ln (4) - \frac{t}{c} ln (e)

\frac{t}{c} ln (e) = \frac{t}{c}

= ln (4) - \frac{t}{c}

ln (4) = 2 ln (2)

= 2 ln (2) - \frac{t}{c}

Popular Examples

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3 lo g_{10} (X) - 4 lo g_{10} (y)

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ln (- 6 \cdot e^{- x})

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3.36 + lo g_{10} (\frac{x}{0.5})

Frequently Asked Questions (FAQ)

What is ln(4e^{-t/c}) ?
The solution to ln(4e^{-t/c}) is 2ln(2)-t/c