What is log_{4}(x^2-49)-5log_{4}(x+7) ?

The solution to log_{4}(x^2-49)-5log_{4}(x+7) is log_{4}((x-7)/((x+7)^4))

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simplify log_{4}(x^2-49)-5log_{4}(x+7)

simplify

lo g_{4} (x^{2} - 49) - 5 lo g_{4} (x + 7)

lo g_{4} (\frac{x - 7}{( x + 7 ) ^{4}})

Solution steps

lo g_{4} (x^{2} - 49) - 5 lo g_{4} (x + 7)

Apply log rule:

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

- 5 lo g_{4} (x + 7) = - lo g_{4} ((x + 7)^{5})

= lo g_{4} (x^{2} - 49) - lo g_{4} ((x + 7)^{5})

Apply log rule:

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

lo g_{4} (x^{2} - 49) - lo g_{4} ((x + 7)^{5}) = lo g_{4} (\frac{x ^{2} - 49}{( x + 7 ) ^{5}})

= lo g_{4} (\frac{x ^{2} - 49}{( x + 7 ) ^{5}})

Simplify

\frac{x ^{2} - 49}{( x + 7 ) ^{5}} : \frac{x - 7}{( x + 7 ) ^{4}}

= lo g_{4} (\frac{x - 7}{( x + 7 ) ^{4}})

- 2 + 3 (\frac{5}{6}) \geq \frac{1}{3}

\frac{10}{45}

\frac{4}{5} - \frac{1}{2}

y^{2} + 12 y + 20 = 0

3 = \frac{x}{2}

What is log_{4}(x^2-49)-5log_{4}(x+7) ?
The solution to log_{4}(x^2-49)-5log_{4}(x+7) is log_{4}((x-7)/((x+7)^4))