What is log_{6}(sqrt(x))-log_{6}(x^6) ?

The solution to log_{6}(sqrt(x))-log_{6}(x^6) is log_{6}((sqrt(x))/(x^6))

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simplify log_{6}(sqrt(x))-log_{6}(x^6)

simplify

lo g_{6} (x) - lo g_{6} (x^{6})

lo g_{6} (\frac{x}{x ^{6}})

Solution steps

lo g_{6} (x) - lo g_{6} (x^{6})

Apply log rule:

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

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

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

ln (x^{2} - 9) - ln (4 - x^{2})

ln ∣ x ∣ + ln ∣ y ∣

\frac{1}{2} lo g_{2} (x) + lo g_{2} (y)

\frac{1}{2} lo g_{10} (9) + 3 lo g_{10} (2)

- \frac{1}{3} ln (8) + 2 ln (5)

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