en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((e^{xln(2)})/2)

Solution

simplify

ln (\frac{e ^{x l n (2)}}{2})

Solution

ln (2) x - ln (2)

Solution steps

ln (\frac{e ^{x l n (2)}}{2})

Apply log rule:

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

ln (\frac{e ^{x l n (2)}}{2}) = ln (e^{x l n (2)}) - ln (2)

= ln (e^{l n (2) x}) - ln (2)

Apply log rule:

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

ln (e^{x l n (2)}) = x ln (2) ln (e)

= x ln (2) ln (e) - ln (2)

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

= ln (2) x - ln (2)

Popular Examples

expand ln(ysqrt(y/(1-y)))expand

ln (y \frac{y}{1 - y})

simplify ln(3/7)simplify

ln (\frac{3}{7})

domain of f(x)=log_{10}(100000x)domain

f (x) = lo g_{10} (100000 x)

simplify log_{10}(25x)-log_{10}(15x)+log_{10}(3y)simplify

lo g_{10} (25 x) - lo g_{10} (15 x) + lo g_{10} (3 y)

simplify log_{10}(x^2y^5)simplify

lo g_{10} (x^{2} y^{5})

Frequently Asked Questions (FAQ)

What is ln((e^{xln(2)})/2) ?
The solution to ln((e^{xln(2)})/2) is ln(2)x-ln(2)