What is log_{4}(x^2-1)-5log_{4}(x+1) ?

The solution to log_{4}(x^2-1)-5log_{4}(x+1) is log_{4}((x-1)/((x+1)^4))

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simplify log_{4}(x^2-1)-5log_{4}(x+1)

simplify

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x + 1)

lo g_{4} (\frac{x - 1}{( x + 1 ) ^{4}})

Solution steps

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x + 1)

Apply log rule:

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

- 5 lo g_{4} (x + 1) = - lo g_{4} ((x + 1)^{5})

= lo g_{4} (x^{2} - 1) - lo g_{4} ((x + 1)^{5})

Apply log rule:

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

lo g_{4} (x^{2} - 1) - lo g_{4} ((x + 1)^{5}) = lo g_{4} (\frac{x ^{2} - 1}{( x + 1 ) ^{5}})

= lo g_{4} (\frac{x ^{2} - 1}{( x + 1 ) ^{5}})

Simplify

\frac{x ^{2} - 1}{( x + 1 ) ^{5}} : \frac{x - 1}{( x + 1 ) ^{4}}

= lo g_{4} (\frac{x - 1}{( x + 1 ) ^{4}})

lo g_{10} (x) - 2 lo g_{10} (y) + 3 lo g_{10} (z)

lo g_{10} (2 x y)

ln (x^{5}) - ln (x) + ln (\frac{1}{x})

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

lo g_{5} (5 x)

What is log_{4}(x^2-1)-5log_{4}(x+1) ?
The solution to log_{4}(x^2-1)-5log_{4}(x+1) is log_{4}((x-1)/((x+1)^4))