What is log_{4}(x^2-25)-4log_{4}(x+5) ?

The solution to log_{4}(x^2-25)-4log_{4}(x+5) is log_{4}((x-5)/((x+5)^3))

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simplify log_{4}(x^2-25)-4log_{4}(x+5)

simplify

lo g_{4} (x^{2} - 25) - 4 lo g_{4} (x + 5)

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

Solution steps

lo g_{4} (x^{2} - 25) - 4 lo g_{4} (x + 5)

Apply log rule:

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

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

= lo g_{4} (x^{2} - 25) - lo g_{4} ((x + 5)^{4})

Apply log rule:

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

lo g_{4} (x^{2} - 25) - lo g_{4} ((x + 5)^{4}) = lo g_{4} (\frac{x ^{2} - 25}{( x + 5 ) ^{4}})

= lo g_{4} (\frac{x ^{2} - 25}{( x + 5 ) ^{4}})

Simplify

\frac{x ^{2} - 25}{( x + 5 ) ^{4}} : \frac{x - 5}{( x + 5 ) ^{3}}

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

lo g_{10} (\frac{x}{3})

\frac{1}{3} ln (3)

ln (\frac{8}{9})

lo g_{10} (1 0^{\frac{1}{2}} (0.1 a)^{\frac{1}{2}}) - 1

lo g_{8} (x^{4})

What is log_{4}(x^2-25)-4log_{4}(x+5) ?
The solution to log_{4}(x^2-25)-4log_{4}(x+5) is log_{4}((x-5)/((x+5)^3))