en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify log_{e}(5e^{2x})

Solution

simplify

lo g_{e} (5 e^{2 x})

Solution

ln (5) + 2 x

Solution steps

lo g_{e} (5 e^{2 x})

Apply log rule:

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

lo g_{e} (5 e^{2 x}) = lo g_{e} (5) + lo g_{e} (e^{2 x})

= lo g_{e} (5) + lo g_{e} (e^{2 x})

Apply log rule:

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

lo g_{e} (e^{2 x}) = 2 x lo g_{e} (e)

= lo g_{e} (5) + 2 x lo g_{e} (e)

lo g_{e} (5) = ln (5)

2 x lo g_{e} (e) = 2 x

= ln (5) + 2 x

Popular Examples

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

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

simplify 3ln(x)-ln(x+1)simplify

3 ln (x) - ln (x + 1)

simplify ln((x-2)/(x+1))simplify

ln (\frac{x - 2}{x + 1})

simplify ln(6)e^3-ln(2)e^{-5}simplify

ln (6) e^{3} - ln (2) e^{- 5}

simplify ln(Csqrt(x^2+y^2))simplify

ln (C x^{2} + y^{2})

Frequently Asked Questions (FAQ)

What is log_{e}(5e^{2x}) ?
The solution to log_{e}(5e^{2x}) is ln(5)+2x