What is expand log_{6}((((xy)^6)/z)^4) ?

The solution to expand log_{6}((((xy)^6)/z)^4) is 4(6log_{6}(xy)-log_{6}(z))

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expand log_{6}((((xy)^6)/z)^4)

expand

lo g_{6} (\frac{( x y ) ^{6}}{z})^{4}

4 (6 lo g_{6} (x y) - lo g_{6} (z))

Solution steps

lo g_{6} (\frac{( x y ) ^{6}}{z})^{4}

Apply log rule:

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

lo g_{6} (\frac{( x y ) ^{6}}{z})^{4} = 4 lo g_{6} (\frac{( x y ) ^{6}}{z})

= 4 lo g_{6} (\frac{( x y ) ^{6}}{z})

Apply log rule:

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

lo g_{6} (\frac{( x y ) ^{6}}{z}) = lo g_{6} ((x y)^{6}) - lo g_{6} (z)

= 4 (- lo g_{6} (z) + lo g_{6} ((x y)^{6}))

Apply log rule:

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

lo g_{6} ((x y)^{6}) = 6 lo g_{6} (x y)

= 4 (6 lo g_{6} (x y) - lo g_{6} (z))

ln (\frac{e ^{4 x}}{x ^{2} + 1})

ln (6.56 \cdot 1 0^{- 4})

ln (6) + ln (\frac{e ^{(2.29928)}}{3})

lo g_{2} (8^{7})

- \frac{1}{0.71} ln (\frac{0.23}{0.72})

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