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Popular >

simplify ln(sqrt(2)e^{2t})

Solution

simplify

ln (2 e^{2 t})

Solution

\frac{1}{2} ln (2) + 2 t

Solution steps

ln (2 e^{2 t})

Apply log rule:

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

ln (2 e^{2 t}) = ln (2) + ln (e^{2 t})

= ln (2) + ln (e^{2 t})

Apply log rule:

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

ln (e^{2 t}) = 2 t ln (e)

= ln (2) + 2 t ln (e)

ln (2) = \frac{1}{2} ln (2)

2 t ln (e) = 2 t

= \frac{1}{2} ln (2) + 2 t

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Frequently Asked Questions (FAQ)

What is ln(sqrt(2)e^{2t}) ?
The solution to ln(sqrt(2)e^{2t}) is 1/2 ln(2)+2t