What is 2log_{10}(x+3)-log_{10}(x-2) ?

The solution to 2log_{10}(x+3)-log_{10}(x-2) is log_{10}(((x+3)^2)/(x-2))

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simplify 2log_{10}(x+3)-log_{10}(x-2)

simplify

2 lo g_{10} (x + 3) - lo g_{10} (x - 2)

lo g_{10} (\frac{( x + 3 ) ^{2}}{x - 2})

Solution steps

2 lo g_{10} (x + 3) - lo g_{10} (x - 2)

Apply log rule:

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

2 lo g_{10} (x + 3) = lo g_{10} ((x + 3)^{2})

= lo g_{10} ((x + 3)^{2}) - lo g_{10} (x - 2)

Apply log rule:

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

lo g_{10} ((x + 3)^{2}) - lo g_{10} (x - 2) = lo g_{10} (\frac{( x + 3 ) ^{2}}{x - 2})

= lo g_{10} (\frac{( x + 3 ) ^{2}}{x - 2})

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What is 2log_{10}(x+3)-log_{10}(x-2) ?
The solution to 2log_{10}(x+3)-log_{10}(x-2) is log_{10}(((x+3)^2)/(x-2))