What is log_{6}(x^6)-log_{6}(2x^2)-log_{6}(x^3) ?

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

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simplify log_{6}(x^6)-log_{6}(2x^2)-log_{6}(x^3)

simplify

lo g_{6} (x^{6}) - lo g_{6} (2 x^{2}) - lo g_{6} (x^{3})

lo g_{6} (\frac{x}{2})

Solution steps

lo g_{6} (x^{6}) - lo g_{6} (2 x^{2}) - lo g_{6} (x^{3})

Apply log rule:

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

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

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

Simplify

\frac{x ^{6}}{2 x ^{2}} : \frac{x ^{4}}{2}

= lo g_{6} (\frac{x ^{4}}{2}) - lo g_{6} (x^{3})

Apply log rule:

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

lo g_{6} (\frac{x ^{4}}{2}) - lo g_{6} (x^{3}) = lo g_{6} (\frac{\frac{x ^{4}}{2}}{x ^{3}})

= lo g_{6} (\frac{\frac{x ^{4}}{2}}{x ^{3}})

Simplify

\frac{\frac{x ^{4}}{2}}{x ^{3}} : \frac{x}{2}

= lo g_{6} (\frac{x}{2})

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