What is the answer to log_{e}(x)+log_{e}(x+2)=3 ?

The answer to log_{e}(x)+log_{e}(x+2)=3 is x=(-2+sqrt(4+4e^3))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

log_{e}(x)+log_{e}(x+2)=3

lo g_{e} (x) + lo g_{e} (x + 2) = 3

x = \frac{- 2 + 4 + 4 e ^{3}}{2}

Decimal Notation

x = 3.59189 \dots

Solution steps

lo g_{e} (x) + lo g_{e} (x + 2) = 3

Apply log rules

x (x + 2) = e^{3}

Solve

x (x + 2) = e^{3} : x = \frac{- 2 + 4 + 4 e ^{3}}{2}, x = \frac{- 2 - 4 + 4 e ^{3}}{2}

x = \frac{- 2 + 4 + 4 e ^{3}}{2}, x = \frac{- 2 - 4 + 4 e ^{3}}{2}

Verify Solutions:

x = \frac{- 2 + 4 + 4 e ^{3}}{2}

True

, x = \frac{- 2 - 4 + 4 e ^{3}}{2}

False

The solution is

x = \frac{- 2 + 4 + 4 e ^{3}}{2}

y, ln (y) = ln (x) + 2

lo g_{10} (x) + lo g_{10} (x + 10) = 3

ln (ln (x - 1)) = e

lo g_{10} (x) = 1 + lo g_{10} (3 x - 4)

lo g_{\frac{1}{2}} (5 (x - 1)) = 3

What is the answer to log_{e}(x)+log_{e}(x+2)=3 ?
The answer to log_{e}(x)+log_{e}(x+2)=3 is x=(-2+sqrt(4+4e^3))/2