What is expand log_{2}(((6^4)/(11))^5) ?

The solution to expand log_{2}(((6^4)/(11))^5) is 5(4log_{2}(6)-log_{2}(11))

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expand log_{2}(((6^4)/(11))^5)

expand

lo g_{2} ((\frac{6 ^{4}}{11})^{5})

5 (4 lo g_{2} (6) - lo g_{2} (11))

Decimal Notation

34.40209 \dots

Solution steps

lo g_{2} ((\frac{6 ^{4}}{11})^{5})

Apply log rule:

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

lo g_{2} ((\frac{6 ^{4}}{11})^{5}) = 5 lo g_{2} (\frac{6 ^{4}}{11})

= 5 lo g_{2} (\frac{6 ^{4}}{11})

Apply log rule:

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

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

= 5 (lo g_{2} (6^{4}) - lo g_{2} (11))

Apply log rule:

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

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

= 5 (4 lo g_{2} (6) - lo g_{2} (11))

lo g_{10} (2 ab)

ln (ye)

ln (2) + 2 ln (x) - ln (9) - 5 ln (y) - 6 ln (z - 4)

ln (\frac{\frac{y}{x}}{\frac{y}{x} + 1})

lo g_{5} (5 x)

What is expand log_{2}(((6^4)/(11))^5) ?
The solution to expand log_{2}(((6^4)/(11))^5) is 5(4log_{2}(6)-log_{2}(11))