en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln((1+bt)e^{-bt})

Solution

simplify

ln ((1 + b t) e^{- b t})

Solution

ln (1 + b t) - b t

Solution steps

ln ((1 + b t) e^{- b t})

Apply log rule:

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

ln ((1 + b t) e^{- b t}) = ln (1 + b t) + ln (e^{- b t})

= ln (b t + 1) + ln (e^{- b t})

Apply log rule:

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

ln (e^{- b t}) = - b t ln (e)

= ln (1 + b t) - b t ln (e)

b t ln (e) = b t

= ln (b t + 1) - b t

Popular Examples

simplify ln(3e^3)+ln(2/(3e^2))simplify

ln (3 e^{3}) + ln (\frac{2}{3 e ^{2}})

simplify ln((1/2)/1)simplify

ln (\frac{\frac{1}{2}}{1})

simplify 3log_{7}(x)+2log_{7}(z)simplify

3 lo g_{7} (x) + 2 lo g_{7} (z)

simplify log_{a}(bc)+log_{b}(ca)simplify

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

simplify ln(75/49)simplify

ln (\frac{75}{49})

Frequently Asked Questions (FAQ)

What is ln((1+bt)e^{-bt}) ?
The solution to ln((1+bt)e^{-bt}) is ln(1+bt)-bt