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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{2} - 4}{( x + 2 ) ^{4}} : \frac{x - 2}{( x + 2 ) ^{3}}

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

3 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

lo g_{10} (4 x + 9) - lo g_{10} (x)

5 ln (x) + 6 ln (y) - 2 ln (z)

lo g_{2} (k^{2} - 4) - lo g_{2} (k) - 2

2 lo g_{2} (x + 1) - lo g_{2} (x + 3) - lo g_{2} (x - 1)

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