What is expand log_{4}((x^5y)^5) ?

The solution to expand log_{4}((x^5y)^5) is 25log_{4}(x)+5log_{4}(y)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand log_{4}((x^5y)^5)

expand

lo g_{4} ((x^{5} y)^{5})

25 lo g_{4} (x) + 5 lo g_{4} (y)

Solution steps

lo g_{4} ((x^{5} y)^{5})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} ((x^{5} y)^{5}) = 5 lo g_{4} (x^{5} y)

= 5 lo g_{4} (x^{5} y)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

5 lo g_{4} (x^{5} y) = 5 lo g_{4} (x^{5}) + 5 lo g_{4} (y)

= 5 lo g_{4} (x^{5}) + 5 lo g_{4} (y)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} (x^{5}) = 5 lo g_{4} (x)

= 5 \cdot 5 lo g_{4} (x) + 5 lo g_{4} (y)

Multiply the numbers:

5 \cdot 5 = 25

= 25 lo g_{4} (x) + 5 lo g_{4} (y)

lo g_{7} (4) + lo g_{7} (3)

lo g_{2} (5) + lo g_{2} (11)

ln (e^{x} y)

ln (\frac{1}{27})

- \frac{1}{4} ln (2)

What is expand log_{4}((x^5y)^5) ?
The solution to expand log_{4}((x^5y)^5) is 25log_{4}(x)+5log_{4}(y)