What is log_{2}(x^2)-3log_{2}(x+1)+log_{4}(3x) ?

The solution to log_{2}(x^2)-3log_{2}(x+1)+log_{4}(3x) is log_{2}((x^2)/((x+1)^3))+log_{4}(3x)

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simplify log_{2}(x^2)-3log_{2}(x+1)+log_{4}(3x)

simplify

lo g_{2} (x^{2}) - 3 lo g_{2} (x + 1) + lo g_{4} (3 x)

lo g_{2} (\frac{x ^{2}}{( x + 1 ) ^{3}}) + lo g_{4} (3 x)

Solution steps

lo g_{2} (x^{2}) - 3 lo g_{2} (x + 1) + lo g_{4} (3 x)

Apply log rule:

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

3 lo g_{2} (x + 1) = lo g_{2} ((x + 1)^{3})

= lo g_{2} (x^{2}) - lo g_{2} ((x + 1)^{3}) + lo g_{4} (3 x)

Apply log rule:

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

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

= lo g_{2} (\frac{x ^{2}}{( x + 1 ) ^{3}}) + lo g_{4} (3 x)

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

\frac{3}{4} lo g_{2} (\frac{3}{4}) + \frac{1}{4} lo g_{2} (\frac{1}{4})

ln (\frac{x ^{4} y}{z ^{5}})

lo g_{4} ((x y)^{3}) - lo g_{4} (x y)

lo g_{2} (7) - lo g_{2} (5)

What is log_{2}(x^2)-3log_{2}(x+1)+log_{4}(3x) ?
The solution to log_{2}(x^2)-3log_{2}(x+1)+log_{4}(3x) is log_{2}((x^2)/((x+1)^3))+log_{4}(3x)