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})

12 ln (x) + 5 ln (y) - 11 ln (z)

ln (\frac{x + 4}{x ^{2} - 5 x + 6})

ln (\frac{1}{y})

ln (x + y) + ln (x - y) - 2 ln (a)

ln ((e^{z} x^{2} y)^{3})

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))