What is log_{4}(x^2-64)-6log_{4}(x+8) ?

The solution to log_{4}(x^2-64)-6log_{4}(x+8) is log_{4}((x-8)/((x+8)^5))

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simplify log_{4}(x^2-64)-6log_{4}(x+8)

simplify

lo g_{4} (x^{2} - 64) - 6 lo g_{4} (x + 8)

lo g_{4} (\frac{x - 8}{( x + 8 ) ^{5}})

Solution steps

lo g_{4} (x^{2} - 64) - 6 lo g_{4} (x + 8)

Apply log rule:

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

- 6 lo g_{4} (x + 8) = - lo g_{4} ((x + 8)^{6})

= lo g_{4} (x^{2} - 64) - lo g_{4} ((x + 8)^{6})

Apply log rule:

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

lo g_{4} (x^{2} - 64) - lo g_{4} ((x + 8)^{6}) = lo g_{4} (\frac{x ^{2} - 64}{( x + 8 ) ^{6}})

= lo g_{4} (\frac{x ^{2} - 64}{( x + 8 ) ^{6}})

Simplify

\frac{x ^{2} - 64}{( x + 8 ) ^{6}} : \frac{x - 8}{( x + 8 ) ^{5}}

= lo g_{4} (\frac{x - 8}{( x + 8 ) ^{5}})

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What is log_{4}(x^2-64)-6log_{4}(x+8) ?
The solution to log_{4}(x^2-64)-6log_{4}(x+8) is log_{4}((x-8)/((x+8)^5))