What is log_{6}((xy)/(zt)) ?

The solution to log_{6}((xy)/(zt)) is log_{6}(x)+log_{6}(y)-log_{6}(z)-log_{6}(t)

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simplify log_{6}((xy)/(zt))

simplify

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

lo g_{6} (x) + lo g_{6} (y) - lo g_{6} (z) - lo g_{6} (t)

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{6} (z t) = lo g_{6} (z) + lo g_{6} (t)

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

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{6} (z) + lo g_{6} (t)) = - lo g_{6} (z) - lo g_{6} (t)

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

\frac{1}{3} ln (a^{2} b^{4})

lo g_{10} (0.5) + lo g_{10} (98)

lo g_{3} (9 (x^{2} - 9))

lo g_{10} (\frac{a b ^{3}}{c ^{2}})

3 ln (\frac{1}{x})

What is log_{6}((xy)/(zt)) ?
The solution to log_{6}((xy)/(zt)) is log_{6}(x)+log_{6}(y)-log_{6}(z)-log_{6}(t)