en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify 2ln(sqrt(x)e^x)

Solution

simplify

2 ln (x e^{x})

Solution

2 ln (x) + 2 x

Solution steps

2 ln (x e^{x})

Apply log rule:

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

2 ln (x e^{x}) = 2 ln (x) + 2 ln (e^{x})

= 2 ln (x) + 2 ln (e^{x})

Apply log rule:

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

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

= 2 ln (x) + 2 x ln (e)

2 x ln (e) = 2 x

= 2 ln (x) + 2 x

Popular Examples

simplify 6ln(6)-5ln(5)simplify

6 ln (6) - 5 ln (5)

simplify log_{10}(45)+log_{10}(2.5)simplify

lo g_{10} (45) + lo g_{10} (2.5)

simplify x(ln(4)-ln(5))simplify

x (ln (4) - ln (5))

expand ln((x+2)^{tan(x)})expand

ln ((x + 2)^{t a n (x)})

simplify ln(S(t))simplify

ln (S (t))

Frequently Asked Questions (FAQ)

What is 2ln(sqrt(x)e^x) ?
The solution to 2ln(sqrt(x)e^x) is 2ln(sqrt(x))+2x