en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Factor the number:

16 = 4^{2}

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

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{4} (4^{2}) = 2

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

Popular Examples

simplify log_{3}(1/9 mn^2)simplify

lo g_{3} (\frac{1}{9} m n^{2})

simplify ln((x^4y)/7)simplify

ln (\frac{x ^{4} y}{7})

simplify log_{10}((x^4+y)/(1000))simplify

lo g_{10} (\frac{x ^{4} + y}{1000})

simplify log_{10}((x^2)/(sqrt(x)))simplify

lo g_{10} (\frac{x ^{2}}{x})

simplify log_{4}((sqrt(y))/(16))simplify

lo g_{4} (\frac{y}{16})

Frequently Asked Questions (FAQ)

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