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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

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

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

5 lo g_{3} (u) + 6 lo g_{3} (v) + lo g_{3} (w)

lo g_{10} (\frac{x}{z ^{3}})

- lo g_{10} (4.4 \cdot 1 0^{- 6})

ln (\frac{25}{8})

- \frac{3}{8} \cdot lo g_{2} (\frac{3}{8}) - \frac{5}{8} lo g_{2} (\frac{5}{8})

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