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

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

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

expand

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

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

Decimal Notation

- 3.85137 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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})

- lo g_{10} (8.04 \cdot 1 0^{- 8})

ln (\frac{x}{9 + x ^{2}})

2000 ln (\frac{140000}{2100 x}) - 9.8 x

ln (\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}})

ln (- a \cdot e)

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