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Popular >

simplify ln(-5/2 e^{2t})

Solution

simplify

ln (- \frac{5}{2} e^{2 t})

Solution

ln (5) - ln (2) + 2 t

Solution steps

ln (- \frac{5}{2} e^{2 t})

Apply log rule:

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

ln (- \frac{5}{2} e^{2 t}) = ln (\frac{5}{2}) + ln (e^{2 t})

= ln (\frac{5}{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 (\frac{5}{2}) + 2 t ln (e)

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{5}{2}) = ln (5) - ln (2)

= ln (5) - ln (2) + 2 ln (e) t

2 t ln (e) = 2 t

= ln (5) - ln (2) + 2 t

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Frequently Asked Questions (FAQ)

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