simplify ln(2e^3k)

Solution

simplify

ln (2 e^{3} k)

ln (2) + 3 + ln (k)

Solution steps

ln (2 e^{3} k)

Apply log rule:

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

ln (2 e^{3} k) = ln (2) + ln (e^{3}) + ln (k)

= ln (2) + ln (e^{3}) + ln (k)

Apply log rule:

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

ln (e^{3}) = 3 ln (e)

= ln (2) + 3 ln (e) + ln (k)

3 ln (e) = 3

= ln (2) + 3 + ln (k)

ln (\frac{( x ^{5} x ^{2} + 1 )}{( x + 1 ) ^{6}})

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