What is log_{4}(x^2-25)-6log_{4}(x+5) ?

The solution to log_{4}(x^2-25)-6log_{4}(x+5) is log_{4}((x-5)/((x+5)^5))

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simplify log_{4}(x^2-25)-6log_{4}(x+5)

simplify

lo g_{4} (x^{2} - 25) - 6 lo g_{4} (x + 5)

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

Solution steps

lo g_{4} (x^{2} - 25) - 6 lo g_{4} (x + 5)

Apply log rule:

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

- 6 lo g_{4} (x + 5) = - lo g_{4} ((x + 5)^{6})

= lo g_{4} (x^{2} - 25) - lo g_{4} ((x + 5)^{6})

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)^{6}) = lo g_{4} (\frac{x ^{2} - 25}{( x + 5 ) ^{6}})

= lo g_{4} (\frac{x ^{2} - 25}{( x + 5 ) ^{6}})

Simplify

\frac{x ^{2} - 25}{( x + 5 ) ^{6}} : \frac{x - 5}{( x + 5 ) ^{5}}

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

lo g_{a} (\frac{x ^{2}}{y z ^{3}})

\frac{1}{2} (lo g_{5} (x - 8) - lo g_{5} (x))

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

lo g_{10} (1 x)

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27)

What is log_{4}(x^2-25)-6log_{4}(x+5) ?
The solution to log_{4}(x^2-25)-6log_{4}(x+5) is log_{4}((x-5)/((x+5)^5))