en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{2}(32a^3)

Solution

simplify

lo g_{2} (32 a^{3})

Solution

5 + 3 lo g_{2} (a)

Solution steps

lo g_{2} (32 a^{3})

Factor the number:

32 = 2^{5}

= lo g_{2} (2^{5} a^{3})

Apply log rule:

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

lo g_{2} (2^{5} a^{3}) = lo g_{2} (2^{5}) + lo g_{2} (a^{3})

= lo g_{2} (2^{5}) + lo g_{2} (a^{3})

Apply log rule:

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

lo g_{2} (2^{5}) = 5

= 5 + lo g_{2} (a^{3})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{2} (a^{3}) = 3 lo g_{2} (a)

= 5 + 3 lo g_{2} (a)

Popular Examples

simplify log_{3}(7x^2)simplify

lo g_{3} (7 x^{2})

simplify 4x-ln(4x)simplify

4 x - ln (4 x)

simplify-ln(3(1-x))simplify

- ln (3 (1 - x))

simplify 4log_{10}(2)+3log_{10}(x)simplify

4 lo g_{10} (2) + 3 lo g_{10} (x)

simplify 4ln(x+3)-1/5 ln(4x+7)simplify

4 ln (x + 3) - \frac{1}{5} ln (4 x + 7)

Frequently Asked Questions (FAQ)

What is log_{2}(32a^3) ?
The solution to log_{2}(32a^3) is 5+3log_{2}(a)