en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

simplify

ln (- 3 e^{- x})

Solution

ln (3) - x

Solution steps

ln (- 3 e^{- x})

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (3) - x ln (e)

x ln (e) = x

= ln (3) - x

Popular Examples

simplify-log_{10}(4.5*10^{-10})simplify

- lo g_{10} (4.5 \cdot 1 0^{- 10})

simplify log_{5}(1/500)simplify

lo g_{5} (\frac{1}{500})

simplify ln(x)+1/2*ln(1+(y^2)/(x^2))simplify

ln (x) + \frac{1}{2} \cdot ln (1 + \frac{y ^{2}}{x ^{2}})

simplify log_{5}(3)+4log_{5}(y)simplify

lo g_{5} (3) + 4 lo g_{5} (y)

join 2/3 log_{10}(2)join

\frac{2}{3} lo g_{10} (2)

Frequently Asked Questions (FAQ)

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