What is log_{4}(x^2-9)-6log_{4}(x+3) ?

The solution to log_{4}(x^2-9)-6log_{4}(x+3) is log_{4}((x-3)/((x+3)^5))

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simplify log_{4}(x^2-9)-6log_{4}(x+3)

simplify

lo g_{4} (x^{2} - 9) - 6 lo g_{4} (x + 3)

lo g_{4} (\frac{x - 3}{( x + 3 ) ^{5}})

Solution steps

lo g_{4} (x^{2} - 9) - 6 lo g_{4} (x + 3)

Apply log rule:

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

- 6 lo g_{4} (x + 3) = - lo g_{4} ((x + 3)^{6})

= lo g_{4} (x^{2} - 9) - lo g_{4} ((x + 3)^{6})

Apply log rule:

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

lo g_{4} (x^{2} - 9) - lo g_{4} ((x + 3)^{6}) = lo g_{4} (\frac{x ^{2} - 9}{( x + 3 ) ^{6}})

= lo g_{4} (\frac{x ^{2} - 9}{( x + 3 ) ^{6}})

Simplify

\frac{x ^{2} - 9}{( x + 3 ) ^{6}} : \frac{x - 3}{( x + 3 ) ^{5}}

= lo g_{4} (\frac{x - 3}{( x + 3 ) ^{5}})

- lo g_{b} (\frac{1}{7})

lo g_{5} (4) + lo g_{5} (\frac{4}{125})

ln (9 e)

ln (\frac{e x}{y}) - ln (\frac{y}{e x})

ln (z) - ln (x) - ln (y)

What is log_{4}(x^2-9)-6log_{4}(x+3) ?
The solution to log_{4}(x^2-9)-6log_{4}(x+3) is log_{4}((x-3)/((x+3)^5))