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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

Simplify

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

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

ln (x \cdot y)

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

lo g_{2} (16 x y^{3}) - lo g_{2} (4 x y)

lo g_{a} (x y)

lo g_{10} (16 x)

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