What is 1/2 ln((x+1)/(x-1))+e^{sin(x^2)}+ln(3) ?

The solution to 1/2 ln((x+1)/(x-1))+e^{sin(x^2)}+ln(3) is ln(((x+1)/(x-1))^{1/2}*3)+e^{sin(x^2)}

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simplify 1/2 ln((x+1)/(x-1))+e^{sin(x^2)}+ln(3)

simplify

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n (x^{2})} + ln (3)

ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}} \cdot 3) + e^{s i n (x^{2})}

Solution steps

\frac{1}{2} ln (\frac{x + 1}{x - 1}) + e^{s i n (x^{2})} + ln (3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}}) + e^{s i n (x^{2})} + ln (3)

Apply log rule:

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

ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}}) + ln (3) = ln (3 (\frac{x + 1}{x - 1})^{\frac{1}{2}})

= ln ((\frac{x + 1}{x - 1})^{\frac{1}{2}} \cdot 3) + e^{s i n (x^{2})}

ln (x^{4})

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ln (0.15) - ln (0.25)

lo g_{b} (z^{4} y)

lo g_{10} (1000 x^{4} y^{6})

What is 1/2 ln((x+1)/(x-1))+e^{sin(x^2)}+ln(3) ?
The solution to 1/2 ln((x+1)/(x-1))+e^{sin(x^2)}+ln(3) is ln(((x+1)/(x-1))^{1/2}*3)+e^{sin(x^2)}