What is expand log_{4}(((12)/(11^3))^6) ?

The solution to expand log_{4}(((12)/(11^3))^6) is 6(log_{4}(12)-3log_{4}(11))

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expand log_{4}(((12)/(11^3))^6)

expand

lo g_{4} ((\frac{12}{1 1 ^{3}})^{6})

6 (lo g_{4} (12) - 3 lo g_{4} (11))

Decimal Notation

- 20.37999 \dots

Solution steps

lo g_{4} ((\frac{12}{1 1 ^{3}})^{6})

Apply log rule:

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

lo g_{4} ((\frac{12}{1 1 ^{3}})^{6}) = 6 lo g_{4} (\frac{12}{1 1 ^{3}})

= 6 lo g_{4} (\frac{12}{1 1 ^{3}})

Apply log rule:

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

lo g_{4} (\frac{12}{1 1 ^{3}}) = lo g_{4} (12) - lo g_{4} (1 1^{3})

= 6 (lo g_{4} (12) - lo g_{4} (1 1^{3}))

Apply log rule:

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

lo g_{4} (1 1^{3}) = 3 lo g_{4} (11)

= 6 (lo g_{4} (12) - 3 lo g_{4} (11))

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

- 0.38 \cdot lo g_{2} (0.38) - 0.62 lo g_{2} (0.62)

2 \cdot ln (\frac{1}{0.8})

lo g_{e} (\frac{1}{5})

ln (1 \cdot 1 0^{10})

What is expand log_{4}(((12)/(11^3))^6) ?
The solution to expand log_{4}(((12)/(11^3))^6) is 6(log_{4}(12)-3log_{4}(11))