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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

4 lo g_{10} (3 x) - 2 lo g_{10} (y)

3 ln (x) + 2 ln (y) - 5 ln (z)

4 lo g_{9} (6) - lo g_{9} (3)

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