What is ln((K^{3/4}L)/(sqrt(K)+1)) ?

The solution to ln((K^{3/4}L)/(sqrt(K)+1)) is 3/4 ln(K)+ln(L)-ln(sqrt(K)+1)

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simplify ln((K^{3/4}L)/(sqrt(K)+1))

simplify

ln (\frac{K ^{\frac{3}{4}} L}{K + 1})

\frac{3}{4} ln (K) + ln (L) - ln (K + 1)

Solution steps

ln (\frac{K ^{\frac{3}{4}} L}{K + 1})

Apply log rule:

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

ln (\frac{K ^{\frac{3}{4}} L}{K + 1}) = ln (K^{\frac{3}{4}} L) - ln (K + 1)

= ln (L K^{\frac{3}{4}}) - ln (K + 1)

Apply log rule:

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

ln (K^{\frac{3}{4}} L) = ln (K^{\frac{3}{4}}) + ln (L)

= ln (K^{\frac{3}{4}}) + ln (L) - ln (K + 1)

Apply log rule:

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

ln (K^{\frac{3}{4}}) = \frac{3}{4} ln (K)

= \frac{3}{4} ln (K) + ln (L) - ln (K + 1)

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12 (ln ∣ (4) + 2 ∣ - ln ∣ (4) + 3 ∣) + C

y [ln (2 y) - ln (1 - 2 y)] - y [ln (y) - ln (1 - y)]

What is ln((K^{3/4}L)/(sqrt(K)+1)) ?
The solution to ln((K^{3/4}L)/(sqrt(K)+1)) is 3/4 ln(K)+ln(L)-ln(sqrt(K)+1)