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

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

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simplify log_{2}(1/x)-log_{2}(1/(x^2))

simplify

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

lo g_{2} (x)

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{\frac{1}{x}}{\frac{1}{x ^{2}}} : x

= lo g_{2} (x)

lo g_{10} (\frac{y ^{3}}{2 x})

\frac{4}{5} ln (x) - 2 ln (y^{4}) + 5 ln (w) - 7 ln (z)

lo g_{2} (5) + lo g_{2} (3)

lo g_{b} (\frac{x ^{3} y}{z ^{4}})

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