What is log_{2}((4pi^2)/(30)) ?

The solution to log_{2}((4pi^2)/(30)) is 2+2log_{2}(pi)-log_{2}(30)

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simplify log_{2}((4pi^2)/(30))

simplify

lo g_{2} (\frac{4 π ^{2}}{30})

2 + 2 lo g_{2} (π) - lo g_{2} (30)

Decimal Notation

0.39610 \dots

Solution steps

lo g_{2} (\frac{4 π ^{2}}{30})

Apply log rule:

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

lo g_{2} (\frac{4 π ^{2}}{30}) = lo g_{2} (4 π^{2}) - lo g_{2} (30)

= lo g_{2} (4 π^{2}) - lo g_{2} (30)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{2} (4 π^{2}) = lo g_{2} (4) + lo g_{2} (π^{2})

= lo g_{2} (4) + lo g_{2} (π^{2}) - lo g_{2} (30)

Apply log rule:

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

lo g_{2} (π^{2}) = 2 lo g_{2} (π)

= lo g_{2} (4) + 2 lo g_{2} (π) - lo g_{2} (30)

lo g_{2} (4) = 2

= 2 + 2 lo g_{2} (π) - lo g_{2} (30)

ln (3 v + w) - ln (w) + 2 - ln (v)

ln (x^{2}) - ln (2 x)

7 lo g_{2} (y) - 4 lo g_{2} (x)

ln (e^{x} x^{3} (x + 1)^{4})

ln (8) - 2 ln (4)

What is log_{2}((4pi^2)/(30)) ?
The solution to log_{2}((4pi^2)/(30)) is 2+2log_{2}(pi)-log_{2}(30)