What is expand log_{2}((6^4)/(11^6)) ?

The solution to expand log_{2}((6^4)/(11^6)) is 4log_{2}(6)-6log_{2}(11)

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expand log_{2}((6^4)/(11^6))

expand

lo g_{2} (\frac{6 ^{4}}{1 1 ^{6}})

4 lo g_{2} (6) - 6 lo g_{2} (11)

Decimal Notation

- 10.41673 \dots

Solution steps

lo g_{2} (\frac{6 ^{4}}{1 1 ^{6}})

Apply log rule:

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

lo g_{2} (\frac{6 ^{4}}{1 1 ^{6}}) = lo g_{2} (6^{4}) - lo g_{2} (1 1^{6})

= lo g_{2} (6^{4}) - lo g_{2} (1 1^{6})

Apply log rule:

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

lo g_{2} (6^{4}) = 4 lo g_{2} (6)

= 4 lo g_{2} (6) - lo g_{2} (1 1^{6})

Apply log rule:

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

lo g_{2} (1 1^{6}) = 6 lo g_{2} (11)

= 4 lo g_{2} (6) - 6 lo g_{2} (11)

ln (20) - ln (3)

ln (x - 1) - ln (3 x + 2)

ln (\frac{T ^{2} \cdot G}{4 π ^{2}})

ln (\frac{0.1536}{0.64})

\frac{2}{3} ln (11) - \frac{2}{3} ln (8)

What is expand log_{2}((6^4)/(11^6)) ?
The solution to expand log_{2}((6^4)/(11^6)) is 4log_{2}(6)-6log_{2}(11)