en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(bte^{-dt})

Solution

simplify

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

Solution

ln (b) + ln (t) - t d

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

d t ln (e) = t d

= ln (b) + ln (t) - t d

Popular Examples

simplify ln(|x|^2)+2ln|x|simplify

ln (∣ x ∣^{2}) + 2 ln ∣ x ∣

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

x + ln (x) + 5 - ln (2)

simplify log_{10}(x^2-2x+8)-2log_{10}(x)simplify

lo g_{10} (x^{2} - 2 x + 8) - 2 lo g_{10} (x)

simplify ln(1.875)+0.6*ln(1.125)simplify

ln (1.875) + 0.6 \cdot ln (1.125)

simplify ln(8e^{4k})simplify

ln (8 e^{4 k})

Frequently Asked Questions (FAQ)

What is ln(bte^{-dt}) ?
The solution to ln(bte^{-dt}) is ln(b)+ln(t)-td