What is log_{3}((2x-1)/(5x+2)) ?

The solution to log_{3}((2x-1)/(5x+2)) is log_{3}(2x-1)-log_{3}(5x+2)

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simplify log_{3}((2x-1)/(5x+2))

simplify

lo g_{3} (\frac{2 x - 1}{5 x + 2})

lo g_{3} (2 x - 1) - lo g_{3} (5 x + 2)

Solution steps

lo g_{3} (\frac{2 x - 1}{5 x + 2})

Apply log rule:

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

lo g_{3} (\frac{2 x - 1}{5 x + 2}) = lo g_{3} (2 x - 1) - lo g_{3} (5 x + 2)

= lo g_{3} (2 x - 1) - lo g_{3} (5 x + 2)

lo g_{10} (\frac{6 w ^{5}}{x})

ln (\frac{729}{10000})

lo g_{2} (x^{2}) - 5 \cdot lo g_{2} (x) + 4

5 ln (5 x)

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

What is log_{3}((2x-1)/(5x+2)) ?
The solution to log_{3}((2x-1)/(5x+2)) is log_{3}(2x-1)-log_{3}(5x+2)