What is log_{4}(x^2-4)-5log_{4}(x+2) ?

The solution to log_{4}(x^2-4)-5log_{4}(x+2) is log_{4}((x-2)/((x+2)^4))

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simplify log_{4}(x^2-4)-5log_{4}(x+2)

simplify

lo g_{4} (x^{2} - 4) - 5 lo g_{4} (x + 2)

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

Solution steps

lo g_{4} (x^{2} - 4) - 5 lo g_{4} (x + 2)

Apply log rule:

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

- 5 lo g_{4} (x + 2) = - lo g_{4} ((x + 2)^{5})

= lo g_{4} (x^{2} - 4) - lo g_{4} ((x + 2)^{5})

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)^{5}) = lo g_{4} (\frac{x ^{2} - 4}{( x + 2 ) ^{5}})

= lo g_{4} (\frac{x ^{2} - 4}{( x + 2 ) ^{5}})

Simplify

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

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

lo g_{8} (9 r)

\frac{4}{17} ln (x) + \frac{12}{17} ln (y)

- 4 lo g_{6} (2 x)

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

lo g_{4} (x^{2} - 9) - 4 lo g_{4} (x + 3)

What is log_{4}(x^2-4)-5log_{4}(x+2) ?
The solution to log_{4}(x^2-4)-5log_{4}(x+2) is log_{4}((x-2)/((x+2)^4))