What is ln(-(y-2)^2e^{3(x+y)}) ?

The solution to ln(-(y-2)^2e^{3(x+y)}) is 2ln(y-2)+3(x+y)

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simplify ln(-(y-2)^2e^{3(x+y)})

simplify

ln (- (y - 2)^{2} e^{3 (x + y)})

2 ln (y - 2) + 3 (x + y)

Solution steps

ln (- (y - 2)^{2} e^{3 (x + y)})

Apply log rule:

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

ln (- (y - 2)^{2} e^{3 (x + y)}) = ln ((y - 2)^{2}) + ln (e^{3 (x + y)})

= ln ((y - 2)^{2}) + ln (e^{3 (y + x)})

Apply log rule:

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

ln ((y - 2)^{2}) = 2 ln (y - 2)

= 2 ln (y - 2) + ln (e^{3 (x + y)})

Apply log rule:

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

ln (e^{3 (x + y)}) = 3 (x + y) ln (e)

= 2 ln (y - 2) + 3 (x + y) ln (e)

3 (x + y) ln (e) = 3 (x + y)

= 2 ln (y - 2) + 3 (y + x)

4 lo g_{10} (z) - lo g_{10} (x)

20 ln (\frac{87}{34})

ln (n θ^{2 n} x e^{- θ n x})

ln (a - b) - ln (a)

- ln (y) - ln (c)

What is ln(-(y-2)^2e^{3(x+y)}) ?
The solution to ln(-(y-2)^2e^{3(x+y)}) is 2ln(y-2)+3(x+y)