en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(x^3y 1/2)

Solution

simplify

2 ln (x^{3} y \frac{1}{2})

Solution

6 ln (x) + 2 ln (y) - 2 ln (2)

Solution steps

2 ln (x^{3} y \frac{1}{2})

Apply log rule:

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

2 ln (x^{3} y \frac{1}{2}) = 2 ln (x^{3}) + 2 ln (y) + 2 ln (\frac{1}{2})

= 2 ln (x^{3}) + 2 ln (y) + 2 ln (\frac{1}{2})

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

= 2 \cdot 3 ln (x) + 2 ln (y) + 2 ln (\frac{1}{2})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= 2 \cdot 3 ln (x) + 2 ln (y) + 2 (ln (1) - ln (2))

2 \cdot 3 ln (x) = 6 ln (x)

2 (ln (1) - ln (2)) = - 2 ln (2)

= 6 ln (x) + 2 ln (y) - 2 ln (2)

Popular Examples

simplify log_{2}(49.92)-log_{2}(6.24)simplify

lo g_{2} (49.92) - lo g_{2} (6.24)

simplify ln(x/(e^{7x)})simplify

ln (\frac{x}{e ^{7 x}})

join (19ln(8/33))/9 join

\frac{19 ln ( \frac{8}{33} )}{9}

simplify ln(54/60)simplify

ln (\frac{54}{60})

simplify ln((x+1)/(x+3))simplify

ln (\frac{x + 1}{x + 3})

Frequently Asked Questions (FAQ)

What is 2ln(x^3y 1/2) ?
The solution to 2ln(x^3y 1/2) is 6ln(x)+2ln(y)-2ln(2)