en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(x^8e^{-8x})

Solution

simplify

ln (x^{8} e^{- 8 x})

Solution

8 ln (x) - 8 x

Solution steps

ln (x^{8} e^{- 8 x})

Apply log rule:

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

ln (x^{8} e^{- 8 x}) = ln (x^{8}) + ln (e^{- 8 x})

= ln (x^{8}) + ln (e^{- 8 x})

Apply log rule:

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

ln (x^{8}) = 8 ln (x)

= 8 ln (x) + ln (e^{- 8 x})

Apply log rule:

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

ln (e^{- 8 x}) = - 8 x ln (e)

= 8 ln (x) - 8 x ln (e)

8 x ln (e) = 8 x

= 8 ln (x) - 8 x

Popular Examples

simplify 9ln(x-2)-5ln(x)simplify

9 ln (x - 2) - 5 ln (x)

expand log_{3}(30x(3x+4))expand

lo g_{3} (30 x (3 x + 4))

simplify ln((15x^5)/(y^5))simplify

ln (\frac{15 x ^{5}}{y ^{5}})

simplify log_{10}(AB^4)simplify

lo g_{10} (A B^{4})

simplify log_{10}(z^4x)simplify

lo g_{10} (z^{4} x)

Frequently Asked Questions (FAQ)

What is ln(x^8e^{-8x}) ?
The solution to ln(x^8e^{-8x}) is 8ln(x)-8x