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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{2} (8) - lo g_{10} (2 x) - lo g_{10} (2 y)

ln (\frac{e ^{8}}{3})

4 ln (x) - 5 ln (y) - 6 ln (z)

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

ln (2.89755 \cdot 1 0^{50})

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