What is log_{4}(2x^2+x-21)-log_{4}(x-3) ?

The solution to log_{4}(2x^2+x-21)-log_{4}(x-3) is log_{4}(2x+7)

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simplify log_{4}(2x^2+x-21)-log_{4}(x-3)

simplify

lo g_{4} (2 x^{2} + x - 21) - lo g_{4} (x - 3)

lo g_{4} (2 x + 7)

Solution steps

lo g_{4} (2 x^{2} + x - 21) - lo g_{4} (x - 3)

Apply log rule:

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

lo g_{4} (2 x^{2} + x - 21) - lo g_{4} (x - 3) = lo g_{4} (\frac{2 x ^{2} + x - 21}{x - 3})

= lo g_{4} (\frac{2 x ^{2} + x - 21}{x - 3})

Simplify

\frac{2 x ^{2} + x - 21}{x - 3} : 2 x + 7

= lo g_{4} (2 x + 7)

4 lo g_{a} (y) - \frac{1}{2} lo g_{a} (x) + 3 lo g_{a} (w)

f (x) = \frac{1}{3} ln (x + 8) + \frac{1}{2} ln (x - 1)

lo g_{b} (z^{2} x)

ln (\frac{2 ( 1 ) - 3}{3 ( 1 ) - 1})

- 16 ln (2) - e^{2} + 16 ln (- 2) + \frac{160}{3} + \frac{1}{e ^{2}}

What is log_{4}(2x^2+x-21)-log_{4}(x-3) ?
The solution to log_{4}(2x^2+x-21)-log_{4}(x-3) is log_{4}(2x+7)