What is ln(((x-2)^2)/(sqrt(x^2+1))) ?

The solution to ln(((x-2)^2)/(sqrt(x^2+1))) is 2ln(x-2)-ln(sqrt(x^2+1))

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simplify ln(((x-2)^2)/(sqrt(x^2+1)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- lo g_{10} (4.8 \cdot 1 0^{- 11})

- lo g_{10} (3.6 \cdot 1 0^{- 4})

ln (\frac{4417910}{4227865})

ln ((\frac{2 πmk T}{h ^{2}})^{\frac{3}{2}})

\frac{1}{3} ln (16 p) - 3 ln (2 p) - 2 ln (5) p^{4} + 6 ln (q)

What is ln(((x-2)^2)/(sqrt(x^2+1))) ?
The solution to ln(((x-2)^2)/(sqrt(x^2+1))) is 2ln(x-2)-ln(sqrt(x^2+1))