en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(e^{-t}sin(t))

Solution

simplify

ln (e^{- t} sin (t))

Solution

- t + ln (sin (t))

Solution steps

ln (e^{- t} sin (t))

Apply log rule:

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

ln (e^{- t} sin (t)) = ln (e^{- t}) + ln (sin (t))

= ln (e^{- t}) + ln (sin (t))

Apply log rule:

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

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

= - t ln (e) + ln (sin (t))

t ln (e) = t

= - t + ln (sin (t))

Popular Examples

simplify 2*ln(7)-6*ln(z-9)simplify

2 \cdot ln (7) - 6 \cdot ln (z - 9)

simplify 63/17 ln|-4|-63/17 ln|-8|simplify

\frac{63}{17} ln ∣ - 4 ∣ - \frac{63}{17} ln ∣ - 8 ∣

expand log_{8}(3x^3)expand

lo g_{8} (3 x^{3})

simplify log_{1/2}(1/2000)simplify

lo g_{\frac{1}{2}} (\frac{1}{2000})

simplify pi/8 (ln(13)-ln(5))simplify

\frac{π}{8} (ln (13) - ln (5))

Frequently Asked Questions (FAQ)

What is ln(e^{-t}sin(t)) ?
The solution to ln(e^{-t}sin(t)) is -t+ln(sin(t))