What is (5/100)*log_{2}((5/100)/(13/100*43/100)) ?

The solution to (5/100)*log_{2}((5/100)/(13/100*43/100)) is (-log_{2}(20)-log_{2}(559/10000))/(20)

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simplify (5/100)log_{2}((5/100)/(13/10043/100))

simplify

(\frac{5}{100}) \cdot lo g_{2} (\frac{\frac{5}{100}}{\frac{13}{100} \cdot \frac{43}{100}})

\frac{- lo g _{2} ( 20 ) - lo g _{2} ( \frac{559}{10000} )}{20}

Decimal Notation

- 0.00804 \dots

Solution steps

(\frac{5}{100}) lo g_{2} (\frac{\frac{5}{100}}{\frac{13}{100} \cdot \frac{43}{100}})

Apply log rule:

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

lo g_{2} (\frac{\frac{5}{100}}{\frac{13}{100} \cdot \frac{43}{100}}) = lo g_{2} (\frac{5}{100}) - lo g_{2} (\frac{13}{100} \cdot \frac{43}{100})

= \frac{5}{100} (lo g_{2} (\frac{5}{100}) - lo g_{2} (\frac{13}{100} \cdot \frac{43}{100}))

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 ( lo g _{2} ( \frac{5}{100} ) - lo g _{2} ( \frac{13}{100} \cdot \frac{43}{100} ) )}{100}

Cancel the common factor:

5

= \frac{lo g _{2} ( \frac{5}{100} ) - lo g _{2} ( \frac{13}{100} \cdot \frac{43}{100} )}{20}

lo g_{2} (\frac{5}{100}) = - lo g_{2} (20)

= \frac{- lo g _{2} ( 20 ) - lo g _{2} ( \frac{13}{100} \cdot \frac{43}{100} )}{20}

Multiply

\frac{13}{100} \cdot \frac{43}{100} : \frac{559}{10000}

= \frac{- lo g _{2} ( 20 ) - lo g _{2} ( \frac{559}{10000} )}{20}

\frac{1}{2} ln (\frac{157}{93})

ln (\frac{150}{600})

- ln (7) + 2 ln (8) - (- ln (2) + 2 ln (3))

ln (x^{2} - 9) - ln (x + 3) + 2 ln (x)

ln (\frac{288}{353})

What is (5/100)*log_{2}((5/100)/(13/100*43/100)) ?
The solution to (5/100)*log_{2}((5/100)/(13/100*43/100)) is (-log_{2}(20)-log_{2}(559/10000))/(20)