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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (y^{- 3}) = - 3 ln (y)

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

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

ln (\frac{x + 8}{2}) + 9

ln (10) - ln (20)

ln^{2} (x) - ln (x^{2}) + x ln (x)

lo g_{10} ((2 x - 7) (x^{2} + 5 x - 3))

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