What is log_{10}(x)+log_{10}(x-7)-log_{10}(3) ?

The solution to log_{10}(x)+log_{10}(x-7)-log_{10}(3) is log_{10}((x(x-7))/3)

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simplify log_{10}(x)+log_{10}(x-7)-log_{10}(3)

simplify

lo g_{10} (x) + lo g_{10} (x - 7) - lo g_{10} (3)

lo g_{10} (\frac{x ( x - 7 )}{3})

Solution steps

lo g_{10} (x) + lo g_{10} (x - 7) - lo g_{10} (3)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (x) + lo g_{10} (x - 7) = lo g_{10} (x (x - 7))

= lo g_{10} (x (x - 7)) - lo g_{10} (3)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (x (x - 7)) - lo g_{10} (3) = lo g_{10} (\frac{x ( x - 7 )}{3})

= lo g_{10} (\frac{x ( x - 7 )}{3})

lo g_{2} (x^{4} \frac{y}{z ^{3}})

2 lo g_{2} (x) + lo g_{2} (t)

lo g_{10} (25 x^{3}) + 3 lo g_{10} (\frac{1}{x})

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

- \frac{1}{2} ln (1 + 2)

What is log_{10}(x)+log_{10}(x-7)-log_{10}(3) ?
The solution to log_{10}(x)+log_{10}(x-7)-log_{10}(3) is log_{10}((x(x-7))/3)