en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((e^x+1)/(e^x))

Solution

simplify

ln (\frac{e ^{x} + 1}{e ^{x}})

Solution

ln (e^{x} + 1) - x

Solution steps

ln (\frac{e ^{x} + 1}{e ^{x}})

Apply log rule:

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

ln (\frac{e ^{x} + 1}{e ^{x}}) = ln (e^{x} + 1) - ln (e^{x})

= ln (e^{x} + 1) - ln (e^{x})

Apply log rule:

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

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

= ln (e^{x} + 1) - x ln (e)

x ln (e) = x

= ln (e^{x} + 1) - x

Popular Examples

simplify ln(ye^y)simplify

ln (y e^{y})

simplify-log_{2}(7)+2log_{2}(x)simplify

- lo g_{2} (7) + 2 lo g_{2} (x)

expand ln((e^3)/7)expand

ln (\frac{e ^{3}}{7})

expand log_{3}((3y^4)/(sqrt(yx)))expand

lo g_{3} (\frac{3 y ^{4}}{y x})

simplify 5/2 log_{10}(x)-log_{10}(y)simplify

\frac{5}{2} lo g_{10} (x) - lo g_{10} (y)

Frequently Asked Questions (FAQ)

What is ln((e^x+1)/(e^x)) ?
The solution to ln((e^x+1)/(e^x)) is ln(e^x+1)-x