What is log_{6}(x^2-36)-log_{6}(x-6) ?

The solution to log_{6}(x^2-36)-log_{6}(x-6) is log_{6}(x+6)

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simplify log_{6}(x^2-36)-log_{6}(x-6)

simplify

lo g_{6} (x^{2} - 36) - lo g_{6} (x - 6)

lo g_{6} (x + 6)

Solution steps

lo g_{6} (x^{2} - 36) - 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^{2} - 36) - lo g_{6} (x - 6) = lo g_{6} (\frac{x ^{2} - 36}{x - 6})

= lo g_{6} (\frac{x ^{2} - 36}{x - 6})

Simplify

\frac{x ^{2} - 36}{x - 6} : x + 6

= lo g_{6} (x + 6)

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

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

lo g_{3} (\frac{9 b ^{3} y ^{2} - 7}{y ( x + 7 ) ^{2}})

x (ln^{3} (x) - 3 ln^{2} (x) + 6 ln (x) - 6)

lo g_{10} (x^{2} y^{3})

What is log_{6}(x^2-36)-log_{6}(x-6) ?
The solution to log_{6}(x^2-36)-log_{6}(x-6) is log_{6}(x+6)