What is log_{2}(2x-1)-4log_{4}(x^2)+3log_{2}(x) ?

The solution to log_{2}(2x-1)-4log_{4}(x^2)+3log_{2}(x) is log_{2}((2x-1)/x)

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simplify log_{2}(2x-1)-4log_{4}(x^2)+3log_{2}(x)

simplify

lo g_{2} (2 x - 1) - 4 lo g_{4} (x^{2}) + 3 lo g_{2} (x)

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

Solution steps

lo g_{2} (2 x - 1) - 4 lo g_{4} (x^{2}) + 3 lo g_{2} (x)

Simplify

lo g_{4} (x^{2}) : lo g_{2} (x)

= lo g_{2} (2 x - 1) - 4 lo g_{2} (x) + 3 lo g_{2} (x)

Add similar elements:

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

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

Apply log rule:

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

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

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

lo g_{10} (\frac{5 y + 1}{y + 4})

ln (\frac{7}{5})

lo g_{10} (3) + lo g_{10} (7)

- lo g_{10} (5 \cdot 1 0^{- 9})

What is log_{2}(2x-1)-4log_{4}(x^2)+3log_{2}(x) ?
The solution to log_{2}(2x-1)-4log_{4}(x^2)+3log_{2}(x) is log_{2}((2x-1)/x)