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

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

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expand ln((xsqrt(x-1))/(x^2+2))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x x - 1) = ln (x) + ln (x - 1)

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

\frac{1}{4} lo g_{b} (x) + 4 lo g_{b} (y) - 2 lo g_{b} (x)

lo g_{b} (\frac{a}{y})

ln (\frac{x}{x + 1})

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

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