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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 lo g_{6} (x + 2) = lo g_{6} ((x + 2)^{2})

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

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

ln (72) - 2 ln (3)

ln (6 m)

ln (u) - ln (u + 1)

- 4 ln (2) - 3 ln (3) - 4 ln (5)

3 ln (+ \frac{1}{3} ln (y))

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