en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{2}((xy)^{10})

Solution

simplify

lo g_{2} ((x y)^{10})

Solution

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

Solution steps

lo g_{2} ((x y)^{10})

Apply log rule

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

lo g_{2} ((x y)^{10}) = 10 lo g_{2} (x y)

= 10 lo g_{2} (x y)

Apply log rule:

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

lo g_{2} (x y) = lo g_{2} (x) + lo g_{2} (y)

= 10 (lo g_{2} (x) + lo g_{2} (y))

Apply the distributive law:

a (b + c) = ab + a c

10 (lo g_{2} (x) + lo g_{2} (y)) = 10 lo g_{2} (x) + 10 lo g_{2} (y)

= 10 lo g_{2} (x) + 10 lo g_{2} (y)

Popular Examples

simplify 20\times 7 simplify

20 \times 7

simplify+7-5/4 simplify

+ 7 - \frac{5}{4}

simplify 4-8^{2/3}simplify

4 - 8^{\frac{2}{3}}

simplify 4\times 4\times 4\times 4\times 4\times 4 simplify

4 \times 4 \times 4 \times 4 \times 4 \times 4

simplify ((3sqrt(5)))/((3sqrt(5)))simplify

\frac{( 3 5 )}{( 3 5 )}

Frequently Asked Questions (FAQ)

What is log_{2}((xy)^{10}) ?
The solution to log_{2}((xy)^{10}) is 10log_{2}(x)+10log_{2}(y)