What is 1/2 log_{2}(3)-2log_{2}(5) ?

The solution to 1/2 log_{2}(3)-2log_{2}(5) is log_{2}((sqrt(3))/(25))

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simplify 1/2 log_{2}(3)-2log_{2}(5)

simplify

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (5)

lo g_{2} (\frac{3}{25})

Decimal Notation

- 3.85137 \dots

Solution steps

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (5)

\frac{1}{2} lo g_{2} (3) = lo g_{2} (3^{\frac{1}{2}})

- 2 lo g_{2} (5) = - lo g_{2} (5^{2})

= lo g_{2} (3^{\frac{1}{2}}) - lo g_{2} (5^{2})

Apply log rule:

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

lo g_{2} (3^{\frac{1}{2}}) - lo g_{2} (5^{2}) = lo g_{2} (\frac{3 ^{\frac{1}{2}}}{5 ^{2}})

= lo g_{2} (\frac{3 ^{\frac{1}{2}}}{5 ^{2}})

5^{2} = 25

= lo g_{2} (\frac{3 ^{\frac{1}{2}}}{25})

Apply exponent rule:

a^{\frac{1}{2}} = a

3^{\frac{1}{2}} = 3

= lo g_{2} (\frac{3}{25})

lo g_{10} (\frac{x ^{5}}{y ^{3}})

lo g_{2} (\frac{8}{x + 4})

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

3 \cdot lo g_{2} (p) + 7 \cdot lo g_{2} (q)

lo g_{7} (x) - lo g_{7} (x^{8})

What is 1/2 log_{2}(3)-2log_{2}(5) ?
The solution to 1/2 log_{2}(3)-2log_{2}(5) is log_{2}((sqrt(3))/(25))