What is log_{2}(2x+1)-5log_{4}(x^2)+4log_{2}(x) ?

The solution to log_{2}(2x+1)-5log_{4}(x^2)+4log_{2}(x) is log_{2}((2x+1)/x)

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simplify log_{2}(2x+1)-5log_{4}(x^2)+4log_{2}(x)

simplify

lo g_{2} (2 x + 1) - 5 lo g_{4} (x^{2}) + 4 lo g_{2} (x)

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

Solution steps

lo g_{2} (2 x + 1) - 5 lo g_{4} (x^{2}) + 4 lo g_{2} (x)

Simplify

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

= lo g_{2} (2 x + 1) - 5 lo g_{2} (x) + 4 lo g_{2} (x)

Add similar elements:

- 5 lo g_{2} (x) + 4 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_{3} ((\frac{3}{x})^{3})

lo g_{10} (3 \cdot 1 0^{x})

lo g_{5} (8) - lo g_{5} (3)

lo g_{3} (28) - lo g_{3} (7)

ln (\frac{x y ^{2}}{e ^{3} z ^{4}})

What is log_{2}(2x+1)-5log_{4}(x^2)+4log_{2}(x) ?
The solution to log_{2}(2x+1)-5log_{4}(x^2)+4log_{2}(x) is log_{2}((2x+1)/x)