en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{4}(16a)

Solution

simplify

lo g_{4} (16 a)

Solution

2 + lo g_{4} (a)

Solution steps

lo g_{4} (16 a)

Factor the number:

16 = 4^{2}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 + lo g_{4} (a)

Popular Examples

simplify 2log_{10}(x)+log_{10}(5)simplify

2 lo g_{10} (x) + lo g_{10} (5)

simplify log_{10}(y)+12log_{10}(z)simplify

lo g_{10} (y) + 12 lo g_{10} (z)

simplify log_{2}((sqrt(x))/8)simplify

lo g_{2} (\frac{x}{8})

expand log_{2}(2x)expand

lo g_{2} (2 x)

simplify log_{10}(y/(100000))simplify

lo g_{10} (\frac{y}{100000})

Frequently Asked Questions (FAQ)

What is log_{4}(16a) ?
The solution to log_{4}(16a) is 2+log_{4}(a)