What is 3/2 ln|x^2+x|+1/2 ln(8) ?

The solution to 3/2 ln|x^2+x|+1/2 ln(8) is ln(2sqrt(2)|x^2+x|^{3/2})

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simplify 3/2 ln|x^2+x|+1/2 ln(8)

simplify

\frac{3}{2} ln x^{2} + x + \frac{1}{2} ln (8)

ln (22 x^{2} + x^{\frac{3}{2}})

Solution steps

\frac{3}{2} ln x^{2} + x + \frac{1}{2} ln (8)

Apply log rule:

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

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

= ln (x^{2} + x^{\frac{3}{2}}) + \frac{1}{2} ln (8)

Apply log rule:

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

\frac{1}{2} ln (8) = ln (8^{\frac{1}{2}})

= ln (x^{2} + x^{\frac{3}{2}}) + ln (8^{\frac{1}{2}})

Apply log rule:

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

ln (x^{2} + x^{\frac{3}{2}}) + ln (8^{\frac{1}{2}}) = ln (8^{\frac{1}{2}} x^{2} + x^{\frac{3}{2}})

= ln (8^{\frac{1}{2}} x^{2} + x^{\frac{3}{2}})

8^{\frac{1}{2}} = 22

= ln (22 x^{2} + x^{\frac{3}{2}})

lo g_{3} (\frac{9}{x + 2})

lo g_{10} (2) 3

5 lo g_{10} (x) + 3 lo g_{10} (y) - 6 lo g_{10} (z)

lo g_{10} (\frac{7}{x})

ln (\frac{e ^{- y} y ^{x}}{x !})

What is 3/2 ln|x^2+x|+1/2 ln(8) ?
The solution to 3/2 ln|x^2+x|+1/2 ln(8) is ln(2sqrt(2)|x^2+x|^{3/2})