What is log_{4}(x^2-16)-log_{4}(x)-log_{4}(x-4) ?

The solution to log_{4}(x^2-16)-log_{4}(x)-log_{4}(x-4) is log_{4}((x+4)/x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{4}(x^2-16)-log_{4}(x)-log_{4}(x-4)

simplify

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

lo g_{4} (\frac{x + 4}{x})

Solution steps

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

Apply log rule:

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

lo g_{4} (x^{2} - 16) - lo g_{4} (x) = lo g_{4} (\frac{x ^{2} - 16}{x})

= lo g_{4} (\frac{x ^{2} - 16}{x}) - lo g_{4} (x - 4)

Apply log rule:

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

lo g_{4} (\frac{x ^{2} - 16}{x}) - lo g_{4} (x - 4) = lo g_{4} (\frac{\frac{x ^{2} - 16}{x}}{x - 4})

= lo g_{4} (\frac{\frac{x ^{2} - 16}{x}}{x - 4})

Simplify

\frac{\frac{x ^{2} - 16}{x}}{x - 4} : \frac{x + 4}{x}

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

lo g_{b} (x^{7} z)

lo g_{a} (\frac{x ^{4}}{y z ^{5}})

lo g_{14} (14 x)

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

ln (x) - ln (x + 2) + ln (2 x - 3)

What is log_{4}(x^2-16)-log_{4}(x)-log_{4}(x-4) ?
The solution to log_{4}(x^2-16)-log_{4}(x)-log_{4}(x-4) is log_{4}((x+4)/x)