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Popular >

simplify ln(1/2 e^4t)

Solution

simplify

ln (\frac{1}{2} e^{4} t)

Solution

ln (t) + 4 - ln (2)

Solution steps

ln (\frac{1}{2} e^{4} t)

Apply log rule:

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

ln (\frac{1}{2} e^{4} t) = ln (\frac{1}{2}) + ln (e^{4}) + ln (t)

= ln (\frac{1}{2}) + ln (e^{4}) + ln (t)

Apply log rule:

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

ln (e^{4}) = 4 ln (e)

= ln (\frac{1}{2}) + 4 ln (e) + ln (t)

Apply log rule:

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

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

= ln (1) - ln (2) + 4 ln (e) + ln (t)

ln (1) = 0

4 ln (e) = 4

= 0 - ln (2) + 4 + ln (t)

Group like terms

= ln (t) - ln (2) + 0 + 4

Add the numbers:

0 + 4 = 4

= ln (t) + 4 - ln (2)

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Frequently Asked Questions (FAQ)

What is ln(1/2 e^4t) ?
The solution to ln(1/2 e^4t) is ln(t)+4-ln(2)