What is log_{10}(x^2sqrt((x+3)/(x-1))) ?

The solution to log_{10}(x^2sqrt((x+3)/(x-1))) is 2log_{10}(x)+log_{10}(sqrt((x+3)/(x-1)))

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simplify log_{10}(x^2sqrt((x+3)/(x-1)))

simplify

lo g_{10} (x^{2} \frac{x + 3}{x - 1})

2 lo g_{10} (x) + lo g_{10} (\frac{x + 3}{x - 1})

Solution steps

lo g_{10} (x^{2} \frac{x + 3}{x - 1})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (x^{2} \frac{x + 3}{x - 1}) = lo g_{10} (x^{2}) + lo g_{10} (\frac{x + 3}{x - 1})

= lo g_{10} (x^{2}) + lo g_{10} (\frac{x + 3}{x - 1})

Simplify

lo g_{10} (x^{2}) : 2 lo g_{10} (x)

= 2 lo g_{10} (x) + lo g_{10} (\frac{x + 3}{x - 1})

\frac{1}{2} lo g_{3} (9 x) + \frac{3}{2} lo g_{3} (4 x^{3})

lo g_{12} (\frac{12}{y})

3 lo g_{10} (6) - 4 lo g_{10} (2) - lo g_{10} (3)

lo g_{2} (\frac{x y ^{2}}{64})

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (7)

What is log_{10}(x^2sqrt((x+3)/(x-1))) ?
The solution to log_{10}(x^2sqrt((x+3)/(x-1))) is 2log_{10}(x)+log_{10}(sqrt((x+3)/(x-1)))