What is log_{4}(x^2-11x+28)-log_{4}(x-7) ?

The solution to log_{4}(x^2-11x+28)-log_{4}(x-7) is log_{4}(x-4)

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simplify log_{4}(x^2-11x+28)-log_{4}(x-7)

simplify

lo g_{4} (x^{2} - 11 x + 28) - lo g_{4} (x - 7)

lo g_{4} (x - 4)

Solution steps

lo g_{4} (x^{2} - 11 x + 28) - lo g_{4} (x - 7)

Apply log rule:

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

lo g_{4} (x^{2} - 11 x + 28) - lo g_{4} (x - 7) = lo g_{4} (\frac{x ^{2} - 11 x + 28}{x - 7})

= lo g_{4} (\frac{x ^{2} - 11 x + 28}{x - 7})

Simplify

\frac{x ^{2} - 11 x + 28}{x - 7} : x - 4

= lo g_{4} (x - 4)

- 3 lo g_{7} (x) + 5 lo g_{7} (y) - lo g_{3} (z)

14 + lo g_{10} (\frac{0.00084}{48})

ln (7 x^{2} - 1) - ln (x^{2})

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

\frac{1}{2} ln ∣ x - 3 ∣ - \frac{1}{x - 3} + \frac{1}{2} ln ∣ x + 3 ∣ + C

What is log_{4}(x^2-11x+28)-log_{4}(x-7) ?
The solution to log_{4}(x^2-11x+28)-log_{4}(x-7) is log_{4}(x-4)