What is ln((16e^{-4sqrt(2)})/((x+1)^2)) ?

The solution to ln((16e^{-4sqrt(2)})/((x+1)^2)) is 4ln(2)-4sqrt(2)-2ln(x+1)

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simplify ln((16e^{-4sqrt(2)})/((x+1)^2))

simplify

ln (\frac{16 e ^{- 42}}{( x + 1 ) ^{2}})

4 ln (2) - 42 - 2 ln (x + 1)

Solution steps

ln (\frac{16 e ^{- 42}}{( x + 1 ) ^{2}})

Apply log rule:

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

ln (\frac{16 e ^{- 42}}{( x + 1 ) ^{2}}) = ln (16 e^{- 42}) - ln ((x + 1)^{2})

= ln (16 e^{- 42}) - ln ((x + 1)^{2})

Apply log rule:

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

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

= ln (16 e^{- 42}) - 2 ln (x + 1)

Apply log rule:

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

ln (16 e^{- 42}) = ln (16) + ln (e^{- 42})

= ln (16) + ln (e^{- 42}) - 2 ln (x + 1)

Apply log rule:

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

ln (e^{- 42}) = - 42 ln (e)

= ln (16) - 42 ln (e) - 2 ln (x + 1)

42 ln (e) = 42

= ln (16) - 42 - 2 ln (x + 1)

ln (16) = 4 ln (2)

= 4 ln (2) - 42 - 2 ln (x + 1)

\frac{8.31 ( 310 )}{0.000995} ln (\frac{100}{5})

0.423 - \frac{0.0592}{2} lo g_{10} (\frac{0.1}{0.075})

ln (x) + 6 ln (y) - 5 ln (z)

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

- 5137.521 + 1239.973 ln (\frac{2015}{30})

What is ln((16e^{-4sqrt(2)})/((x+1)^2)) ?
The solution to ln((16e^{-4sqrt(2)})/((x+1)^2)) is 4ln(2)-4sqrt(2)-2ln(x+1)