What is expand log_{2}(xsqrt(x^2+1)) ?

The solution to expand log_{2}(xsqrt(x^2+1)) is log_{2}(x)+log_{2}(sqrt(x^2+1))

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expand log_{2}(xsqrt(x^2+1))

expand

lo g_{2} (x x^{2} + 1)

lo g_{2} (x) + lo g_{2} (x^{2} + 1)

Solution steps

lo g_{2} (x x^{2} + 1)

Apply log rule:

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

lo g_{2} (x x^{2} + 1) = lo g_{2} (x) + lo g_{2} (x^{2} + 1)

= lo g_{2} (x) + lo g_{2} (x^{2} + 1)

\frac{2}{3} ln (4) - \frac{1}{3} ln (7)

3 lo g_{10} (x^{3}) + lo g_{10} (x) - lo g_{10} (x^{4})

ln (\frac{25}{20})

lo g_{b} (2) + lo g_{b} (3)

- \frac{7}{8} lo g_{2} (\frac{7}{8}) - \frac{1}{8} lo g_{2} (\frac{1}{8})

What is expand log_{2}(xsqrt(x^2+1)) ?
The solution to expand log_{2}(xsqrt(x^2+1)) is log_{2}(x)+log_{2}(sqrt(x^2+1))