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

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

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

expand

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 (\frac{a ^{2}}{b ^{4} c})

lo g_{10} (\frac{10 z}{5})

2 ln (5) - ln (7) + 3 ln (14) - 2 ln (10)

lo g_{a} (x) - 2 lo g_{a} (y)

\frac{48125}{( 2 π ( 98 - 94 ) )} ln (\frac{70}{20})

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