What is 1/2 log_{2}(3)-2log_{2}(7) ?

The solution to 1/2 log_{2}(3)-2log_{2}(7) is log_{2}((sqrt(3))/(49))

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simplify 1/2 log_{2}(3)-2log_{2}(7)

simplify

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (7)

lo g_{2} (\frac{3}{49})

Decimal Notation

- 4.82222 \dots

Solution steps

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (7)

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

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

= lo g_{2} (3^{\frac{1}{2}}) - lo g_{2} (7^{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} (7^{2}) = lo g_{2} (\frac{3 ^{\frac{1}{2}}}{7 ^{2}})

= lo g_{2} (\frac{3 ^{\frac{1}{2}}}{7 ^{2}})

7^{2} = 49

= lo g_{2} (\frac{3 ^{\frac{1}{2}}}{49})

Apply exponent rule:

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

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

= lo g_{2} (\frac{3}{49})

12 lo g_{7} (x) - 3 lo g_{7} (y)

6 + 3 ln (\frac{1}{2})

lo g_{2} (\frac{c d ^{3}}{e ^{4}})

lo g_{10} (8^{2}) - lo g_{10} (12 5^{2})

lo g_{10} (3 (x + 1)^{2})

What is 1/2 log_{2}(3)-2log_{2}(7) ?
The solution to 1/2 log_{2}(3)-2log_{2}(7) is log_{2}((sqrt(3))/(49))