What is log_{2}(sqrt(5))-log_{2}(sqrt(40)) ?

The solution to log_{2}(sqrt(5))-log_{2}(sqrt(40)) is -3/2

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simplify log_{2}(sqrt(5))-log_{2}(sqrt(40))

simplify

lo g_{2} (5) - lo g_{2} (40)

- \frac{3}{2}

Decimal

- 1.5

Solution steps

lo g_{2} (5) - lo g_{2} (40)

Apply log rule:

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

lo g_{2} (5) - lo g_{2} (40) = lo g_{2} (\frac{5}{40})

= lo g_{2} (\frac{5}{40})

\frac{5}{40} = 2^{- \frac{3}{2}}

= lo g_{2} (2^{- \frac{3}{2}})

Apply log rule:

lo g_{a} (a^{b}) = b

= - \frac{3}{2}

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

lo g_{\frac{1}{3}} (\frac{3 x ^{2} - 14 x - 24}{6}) - x + 3

ln (\frac{2 + 1}{2 - 1})

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

- \frac{4}{6} lo g_{2} (\frac{4}{6}) - \frac{2}{6} lo g_{2} (\frac{2}{6})

What is log_{2}(sqrt(5))-log_{2}(sqrt(40)) ?
The solution to log_{2}(sqrt(5))-log_{2}(sqrt(40)) is -3/2