en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(-4e^{-3x})

Solution

simplify

ln (- 4 e^{- 3 x})

Solution

2 ln (2) - 3 x

Solution steps

ln (- 4 e^{- 3 x})

Apply log rule:

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

ln (- 4 e^{- 3 x}) = ln (4) + ln (e^{- 3 x})

= ln (4) + ln (e^{- 3 x})

Apply log rule:

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

ln (e^{- 3 x}) = - 3 x ln (e)

= ln (4) - 3 x ln (e)

3 x ln (e) = 3 x

= ln (4) - 3 x

ln (4) = 2 ln (2)

= 2 ln (2) - 3 x

Popular Examples

simplify ln((x+8)/2)+9 simplify

ln (\frac{x + 8}{2}) + 9

simplify ln(10)-ln(20)simplify

ln (10) - ln (20)

simplify ln^2(x)-ln(x^2)+xln(x)simplify

ln^{2} (x) - ln (x^{2}) + x ln (x)

simplify log_{10}((2x-7)(x^2+5x-3))simplify

lo g_{10} ((2 x - 7) (x^{2} + 5 x - 3))

simplify ln(200.75)-ln(200)simplify

ln (200.75) - ln (200)

Frequently Asked Questions (FAQ)

What is ln(-4e^{-3x}) ?
The solution to ln(-4e^{-3x}) is 2ln(2)-3x