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} (7.3 \cdot 1 0^{- 9})

4 ln (2 z^{2})

(1.0299) \cdot ln (\frac{80}{250}) - (0.41195) ln (\frac{550}{240})

ln (\frac{100 + 150}{150})

182000 \cdot [ln (0.5) - ln (1.3)]

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))