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

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

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simplify log_{e}(xsqrt(x^2+1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{e} (x) = ln (x)

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

Apply log rule:

lo g_{e} (x) = ln (x)

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

- 0.6 \cdot lo g_{2} (0.6) - 0.4 \cdot lo g_{2} (0.4)

- lo g_{10} (6.7 \cdot 1 0^{- 8})

ln (\frac{153.5}{100}) + (\frac{1}{2} \cdot 0. 4^{2} - 0.02) \cdot 4

\frac{1}{2} ln (2 x)

- lo g_{10} (3.75 \cdot 1 0^{2})

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