What is expand log_{2}((8d^4)/(n^3)) ?

The solution to expand log_{2}((8d^4)/(n^3)) is 3+4log_{2}(d)-3log_{2}(n)

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expand log_{2}((8d^4)/(n^3))

expand

lo g_{2} (\frac{8 d ^{4}}{n ^{3}})

3 + 4 lo g_{2} (d) - 3 lo g_{2} (n)

Solution steps

lo g_{2} (\frac{8 d ^{4}}{n ^{3}})

Apply log rule:

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

lo g_{2} (\frac{8 d ^{4}}{n ^{3}}) = lo g_{2} (8 d^{4}) - lo g_{2} (n^{3})

= lo g_{2} (8 d^{4}) - lo g_{2} (n^{3})

Apply log rule:

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

lo g_{2} (n^{3}) = 3 lo g_{2} (n)

= lo g_{2} (8 d^{4}) - 3 lo g_{2} (n)

Apply log rule:

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

lo g_{2} (8 d^{4}) = lo g_{2} (8) + lo g_{2} (d^{4})

= lo g_{2} (8) + lo g_{2} (d^{4}) - 3 lo g_{2} (n)

Apply log rule:

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

lo g_{2} (d^{4}) = 4 lo g_{2} (d)

= lo g_{2} (8) + 4 lo g_{2} (d) - 3 lo g_{2} (n)

lo g_{2} (8) = 3

= 3 + 4 lo g_{2} (d) - 3 lo g_{2} (n)

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

e^{(3^{2} - 1)} \cdot 3^{3} + ln (5 \cdot 3^{3}) \cdot 3^{2} + 15

ln (2 e^{26 x})

\frac{1}{3} ln (\frac{x + 1}{x ^{2} - x + 1})

ln (\frac{56}{1076})

What is expand log_{2}((8d^4)/(n^3)) ?
The solution to expand log_{2}((8d^4)/(n^3)) is 3+4log_{2}(d)-3log_{2}(n)