What is log_{2}((4x+1)/x) ?

The solution to log_{2}((4x+1)/x) is log_{2}(4x+1)-log_{2}(x)

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simplify log_{2}((4x+1)/x)

simplify

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

lo g_{2} (4 x + 1) - lo g_{2} (x)

Solution steps

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

Apply log rule:

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

lo g_{2} (\frac{4 x + 1}{x}) = lo g_{2} (4 x + 1) - lo g_{2} (x)

= lo g_{2} (4 x + 1) - lo g_{2} (x)

2 lo g_{4} (x) - lo g_{4} (y) - \frac{1}{2} lo g_{4} (z)

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

ln (\frac{e ^{x l n (2)}}{2})

lo g_{10} (1000 y)

ln (3 e^{x})

What is log_{2}((4x+1)/x) ?
The solution to log_{2}((4x+1)/x) is log_{2}(4x+1)-log_{2}(x)