What is ln((x+1)^2(dy)/(dx)) ?

The solution to ln((x+1)^2(dy)/(dx)) is 2ln(x+1)+ln((dy)/(dx))

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simplify ln((x+1)^2(dy)/(dx))

simplify

ln ((x + 1)^{2} \frac{d y}{d x})

2 ln (x + 1) + ln (\frac{d y}{d x})

Solution steps

ln ((x + 1)^{2} \frac{d y}{d x})

Apply log rule:

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

ln ((x + 1)^{2} \frac{d y}{d x}) = ln ((x + 1)^{2}) + ln (\frac{d y}{d x})

= ln ((x + 1)^{2}) + ln (\frac{d y}{d x})

Apply log rule:

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

ln ((x + 1)^{2}) = 2 ln (x + 1)

= 2 ln (x + 1) + ln (\frac{d y}{d x})

f (x) = lo g_{2} (x - 4) + 3 lo g_{2} (x)

- lo g_{10} (1.41 x 1 0^{- 11})

4 lo g_{2} (x) + lo g_{2} (3)

ln (- 3 e^{- 4 t})

What is ln((x+1)^2(dy)/(dx)) ?
The solution to ln((x+1)^2(dy)/(dx)) is 2ln(x+1)+ln((dy)/(dx))