What is log_{4}((x^2)/(y^6)) ?

The solution to log_{4}((x^2)/(y^6)) is log_{2}(x)-6log_{4}(y)

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simplify log_{4}((x^2)/(y^6))

simplify

lo g_{4} (\frac{x ^{2}}{y ^{6}})

lo g_{2} (x) - 6 lo g_{4} (y)

Solution steps

lo g_{4} (\frac{x ^{2}}{y ^{6}})

Apply log rule:

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

lo g_{4} (\frac{x ^{2}}{y ^{6}}) = lo g_{4} (x^{2}) - lo g_{4} (y^{6})

= lo g_{4} (x^{2}) - lo g_{4} (y^{6})

lo g_{4} (x^{2}) = lo g_{2} (x)

lo g_{4} (y^{6}) = 6 lo g_{4} (y)

= lo g_{2} (x) - 6 lo g_{4} (y)

lo g_{a} (\frac{1}{64})

- lo g_{10} (5 \cdot 1 0^{- 6})

lo g_{b} (125 k)

lo g_{7} (\frac{x ^{3}}{x - 5})

What is log_{4}((x^2)/(y^6)) ?
The solution to log_{4}((x^2)/(y^6)) is log_{2}(x)-6log_{4}(y)