en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify ln(15*e^{x/T})

Solution

simplify

ln (15 \cdot e^{\frac{x}{T}})

Solution

ln (15) + \frac{x}{T}

Solution steps

ln (15 e^{\frac{x}{T}})

Apply log rule:

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

ln (15 e^{\frac{x}{T}}) = ln (15) + ln (e^{\frac{x}{T}})

= ln (15) + ln (e^{\frac{x}{T}})

Apply log rule:

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

ln (e^{\frac{x}{T}}) = \frac{x}{T} ln (e)

= ln (15) + \frac{x}{T} ln (e)

\frac{x}{T} ln (e) = \frac{x}{T}

= ln (15) + \frac{x}{T}

Popular Examples

simplify ln((e^{-k}*k^x)/(x!))simplify

ln (\frac{e ^{- k} \cdot k ^{x}}{x !})

simplify-5/9 (ln(10-0.9v^2)-ln(10-0.9v_{0}^2))simplify

- \frac{5}{9} (ln (10 - 0.9 v^{2}) - ln (10 - 0.9 v_{0}^{2}))

join 1/2 log_{10}(11)join

\frac{1}{2} lo g_{10} (11)

simplify ln(((x+5)^2)/((x-9)^2(x^2-15)^5))simplify

ln (\frac{( x + 5 ) ^{2}}{( x - 9 ) ^{2} ( x ^{2} - 15 ) ^{5}})

simplify ln(sec(x)cos(y))simplify

ln (sec (x) cos (y))

Frequently Asked Questions (FAQ)

What is ln(15*e^{x/T}) ?
The solution to ln(15*e^{x/T}) is ln(15)+x/T