What is log_{2}(sqrt(x))-log_{2}(x^7) ?

The solution to log_{2}(sqrt(x))-log_{2}(x^7) is log_{2}((sqrt(x))/(x^7))

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simplify log_{2}(sqrt(x))-log_{2}(x^7)

simplify

lo g_{2} (x) - lo g_{2} (x^{7})

lo g_{2} (\frac{x}{x ^{7}})

Solution steps

lo g_{2} (x) - lo g_{2} (x^{7})

Apply log rule:

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

lo g_{2} (x) - lo g_{2} (x^{7}) = lo g_{2} (\frac{x}{x ^{7}})

= lo g_{2} (\frac{x}{x ^{7}})

- \frac{1}{6} lo g_{2} (\frac{1}{6}) - \frac{5}{6} lo g_{2} (\frac{5}{6})

- lo g_{10} (7.4 \cdot 1 0^{- 4})

ln ((x y)^{3})

3 ln (x - 4) + 2 ln (3) - \frac{1}{2} ln (y)

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

What is log_{2}(sqrt(x))-log_{2}(x^7) ?
The solution to log_{2}(sqrt(x))-log_{2}(x^7) is log_{2}((sqrt(x))/(x^7))