What is log_{2}(sqrt(x))-log_{2}(x^8) ?

The solution to log_{2}(sqrt(x))-log_{2}(x^8) is log_{2}((sqrt(x))/(x^8))

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simplify log_{2}(sqrt(x))-log_{2}(x^8)

simplify

lo g_{2} (x) - lo g_{2} (x^{8})

lo g_{2} (\frac{x}{x ^{8}})

Solution steps

lo g_{2} (x) - lo g_{2} (x^{8})

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^{8}) = lo g_{2} (\frac{x}{x ^{8}})

= lo g_{2} (\frac{x}{x ^{8}})

- (\frac{1}{3} lo g_{e} (\frac{1}{3}) + \frac{2}{3} lo g_{e} (\frac{2}{3}))

ln (5 (10)) + e^{- 1.31 (10)}

\frac{1}{7} ln (x - 4) - \frac{1}{7} ln (x + 9)

\frac{8}{6} \cdot ln (\frac{13 \cdot 15 \cdot 17 \cdot 19 \cdot 21 \cdot 23}{1 2 ^{6}})

lo g_{b} (8) - lo g_{b} (4) - 2 lo g_{b} (3)

What is log_{2}(sqrt(x))-log_{2}(x^8) ?
The solution to log_{2}(sqrt(x))-log_{2}(x^8) is log_{2}((sqrt(x))/(x^8))