What is 3/4*log_{2}(((3/4))/((1/20))) ?

The solution to 3/4*log_{2}(((3/4))/((1/20))) is 3/4 (log_{2}(3/4)+log_{2}(20))

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simplify 3/4*log_{2}(((3/4))/((1/20)))

simplify

\frac{3}{4} \cdot lo g_{2} (\frac{( \frac{3}{4} )}{( \frac{1}{20} )})

\frac{3}{4} (lo g_{2} (\frac{3}{4}) + lo g_{2} (20))

Decimal Notation

2.93016 \dots

Solution steps

\frac{3}{4} lo g_{2} (\frac{( \frac{3}{4} )}{( \frac{1}{20} )})

Apply log rule:

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

lo g_{2} (\frac{( \frac{3}{4} )}{( \frac{1}{20} )}) = lo g_{2} ((\frac{3}{4})) - lo g_{2} ((\frac{1}{20}))

= \frac{3}{4} (lo g_{2} (\frac{3}{4}) - lo g_{2} (\frac{1}{20}))

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= \frac{3}{4} (lo g_{2} (\frac{3}{4}) - (- lo g_{2} (20)))

Apply rule

- (- a) = a

= \frac{3}{4} (lo g_{2} (\frac{3}{4}) + lo g_{2} (20))

\frac{8}{π} \cdot ln (6) + \frac{2}{π} \cdot ln (\frac{7}{6})

ln (\frac{( x - 3 )}{( x + 3 )})

0.0004 ln ∣ 2000 ∣ - 0.004 ln ∣ 2000 - 25000 ∣

- 1 ln (- 4) - (- 1) ln (- 5)

2 ln (3 (4) - 2) - ln (2)

What is 3/4*log_{2}(((3/4))/((1/20))) ?
The solution to 3/4*log_{2}(((3/4))/((1/20))) is 3/4 (log_{2}(3/4)+log_{2}(20))