What is log_{6}((x^3y)/(2z^7)) ?

The solution to log_{6}((x^3y)/(2z^7)) is 3log_{6}(x)+log_{6}(y)-log_{6}(2)-7log_{6}(z)

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simplify log_{6}((x^3y)/(2z^7))

simplify

lo g_{6} (\frac{x ^{3} y}{2 z ^{7}})

3 lo g_{6} (x) + lo g_{6} (y) - lo g_{6} (2) - 7 lo g_{6} (z)

Solution steps

lo g_{6} (\frac{x ^{3} y}{2 z ^{7}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{6} (\frac{x ^{3} y}{2 z ^{7}}) = lo g_{6} (x^{3} y) - lo g_{6} (2 z^{7})

= lo g_{6} (x^{3} y) - lo g_{6} (2 z^{7})

lo g_{6} (x^{3} y) = 3 lo g_{6} (x) + lo g_{6} (y)

lo g_{6} (2 z^{7}) = lo g_{6} (2) + 7 lo g_{6} (z)

= 3 lo g_{6} (x) + lo g_{6} (y) - (lo g_{6} (2) + 7 lo g_{6} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{6} (2) + 7 lo g_{6} (z)) = - lo g_{6} (2) - 7 lo g_{6} (z)

= 3 lo g_{6} (x) + lo g_{6} (y) - lo g_{6} (2) - 7 lo g_{6} (z)

- 0.4 + \frac{0.592}{2} \cdot lo g_{10} (\frac{0.2}{1})

\frac{4}{10} lo g_{2} (\frac{10}{4}) + \frac{6}{10} lo g_{2} (\frac{10}{6})

- lo g_{10} (1.1 \cdot 1 0^{- 7})

\frac{1}{4} ln (\frac{38}{13})

ln (\frac{e ^{3} x ^{3} x + 2}{3 y ^{2}})

What is log_{6}((x^3y)/(2z^7)) ?
The solution to log_{6}((x^3y)/(2z^7)) is 3log_{6}(x)+log_{6}(y)-log_{6}(2)-7log_{6}(z)