What is expand log_{6}((3*11)^6) ?

The solution to expand log_{6}((3*11)^6) is 6log_{6}(3)+6log_{6}(11)

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expand log_{6}((3*11)^6)

expand

lo g_{6} ((3 \cdot 11)^{6})

6 lo g_{6} (3) + 6 lo g_{6} (11)

Decimal Notation

11.70862 \dots

Solution steps

lo g_{6} ((3 \cdot 11)^{6})

Apply log rule:

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

lo g_{6} ((3 \cdot 11)^{6}) = 6 lo g_{6} (3 \cdot 11)

= 6 lo g_{6} (3 \cdot 11)

Apply log rule:

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

6 lo g_{6} (3 \cdot 11) = 6 lo g_{6} (3) + 6 lo g_{6} (11)

= 6 lo g_{6} (3) + 6 lo g_{6} (11)

\frac{4 ln ( \frac{54}{7} )}{ln ( 2 )}

ln (\frac{1}{3})

π^{81} (ln (11) - 3 ln (2))

3 lo g_{10} (x) - lo g_{10} (2)

ln (4 x y^{2}) - 2 ln (x^{2} y)

What is expand log_{6}((3*11)^6) ?
The solution to expand log_{6}((3*11)^6) is 6log_{6}(3)+6log_{6}(11)