en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((x+6)/(e^x))

Solution

simplify

ln (\frac{x + 6}{e ^{x}})

Solution

ln (x + 6) - x

Solution steps

ln (\frac{x + 6}{e ^{x}})

Apply log rule:

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

ln (\frac{x + 6}{e ^{x}}) = ln (x + 6) - ln (e^{x})

= ln (x + 6) - ln (e^{x})

Apply log rule:

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

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

= ln (x + 6) - x ln (e)

x ln (e) = x

= ln (x + 6) - x

Popular Examples

simplify log_{12}(+1/2 log_{7}(-log_{2}(x)))simplify

lo g_{12} (+ \frac{1}{2} lo g_{7} (- lo g_{2} (x)))

simplify log_{3}(x^7sqrt(3y^6))simplify

lo g_{3} (x^{7} 3 y^{6})

simplify log_{10}(8(1+3x))simplify

lo g_{10} (8 (1 + 3 x))

simplify log_{10}(m/(10n))simplify

lo g_{10} (\frac{m}{10 n})

simplify log_{10}(3xy^3)simplify

lo g_{10} (3 x y^{3})

Frequently Asked Questions (FAQ)

What is ln((x+6)/(e^x)) ?
The solution to ln((x+6)/(e^x)) is ln(x+6)-x