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Popular >

simplify ln(8e^{4k})

Solution

simplify

ln (8 e^{4 k})

Solution

3 ln (2) + 4 k

Solution steps

ln (8 e^{4 k})

Apply log rule:

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

ln (8 e^{4 k}) = ln (8) + ln (e^{4 k})

= ln (8) + ln (e^{4 k})

Apply log rule:

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

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

= ln (8) + 4 k ln (e)

4 k ln (e) = 4 k

= ln (8) + 4 k

ln (8) = 3 ln (2)

= 3 ln (2) + 4 k

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Frequently Asked Questions (FAQ)

What is ln(8e^{4k}) ?
The solution to ln(8e^{4k}) is 3ln(2)+4k