What is log_{4}(x^2-9)-5log_{4}(x+3) ?

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

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simplify log_{4}(x^2-9)-5log_{4}(x+3)

simplify

lo g_{4} (x^{2} - 9) - 5 lo g_{4} (x + 3)

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

Solution steps

lo g_{4} (x^{2} - 9) - 5 lo g_{4} (x + 3)

Apply log rule:

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

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

= lo g_{4} (x^{2} - 9) - lo g_{4} ((x + 3)^{5})

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)^{5}) = lo g_{4} (\frac{x ^{2} - 9}{( x + 3 ) ^{5}})

= lo g_{4} (\frac{x ^{2} - 9}{( x + 3 ) ^{5}})

Simplify

\frac{x ^{2} - 9}{( x + 3 ) ^{5}} : \frac{x - 3}{( x + 3 ) ^{4}}

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

ln (\frac{7}{8})

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

lo g_{10} (2) + lo g_{10} (x)

3 ln (2) + 2 ln (x) - \frac{1}{2} ln (x + 4)

lo g_{8} (\frac{3 x ^{3}}{( 4 ) ( 3 )})

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