What is log_{2}((e^2)/4) ?

The solution to log_{2}((e^2)/4) is 2log_{2}(e)-2

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simplify log_{2}((e^2)/4)

simplify

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

2 lo g_{2} (e) - 2

Decimal Notation

0.88539 \dots

Solution steps

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

Apply log rule:

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

lo g_{2} (\frac{e ^{2}}{4}) = lo g_{2} (e^{2}) - lo g_{2} (4)

= lo g_{2} (e^{2}) - lo g_{2} (4)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{2} (e^{2}) = 2 lo g_{2} (e)

= 2 lo g_{2} (e) - lo g_{2} (4)

lo g_{2} (4) = 2

= 2 lo g_{2} (e) - 2

ln (2 x + 1) + ln (x - 1) - 2 ln (x)

lo g_{2} (x^{2}) - 3 lo g_{2} (x + 1) + lo g_{4} (3 x)

ln (1 + x) - ln (1 - x)

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

ln (\frac{x ^{4} y}{z ^{5}})