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

The solution to 1/2 log_{2}(5)-2log_{2}(3) is log_{2}((sqrt(5))/9)

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

simplify

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

lo g_{2} (\frac{5}{9})

Decimal Notation

- 2.00896 \dots

Solution steps

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

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

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

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

Apply log rule:

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

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

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

3^{2} = 9

= lo g_{2} (\frac{5 ^{\frac{1}{2}}}{9})

Apply exponent rule:

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

5^{\frac{1}{2}} = 5

= lo g_{2} (\frac{5}{9})

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

lo g_{10} (\frac{x y}{z})

lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (4 x) - lo g_{10} (x)

lo g_{10} (a) + lo g_{10} (b) + lo g_{10} (c)

What is 1/2 log_{2}(5)-2log_{2}(3) ?
The solution to 1/2 log_{2}(5)-2log_{2}(3) is log_{2}((sqrt(5))/9)