What is the answer to ln(x)=1-ln(x+3) ?

The answer to ln(x)=1-ln(x+3) is x=(-3+sqrt(9+4e))/2

Solve for x: ln(x)=1-ln(x+3)

The solution is x=(-3+sqrt(9+4e))/2

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

x = \frac{- 3 + 9 + 4 e}{2}

Decimal

x = 0.72896 \dots

Solution steps

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

Add

ln (x + 3)

to both sides

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

Simplify

ln (x) + ln (x + 3) = 1

Apply log rules

x (x + 3) = e

Solve

x (x + 3) = e : x = \frac{- 3 + 9 + 4 e}{2}, x = \frac{- 3 - 9 + 4 e}{2}

x = \frac{- 3 + 9 + 4 e}{2}, x = \frac{- 3 - 9 + 4 e}{2}

Verify Solutions:

x = \frac{- 3 + 9 + 4 e}{2}

True

, x = \frac{- 3 - 9 + 4 e}{2}

False

The solution is

x = \frac{- 3 + 9 + 4 e}{2}

lo g_{10} (x + 3) = lo g_{10} (2 x + 1)

lo g_{\frac{1}{4}} (3 x + 7) = - 2

lo g_{x} (5) = - 2

y, x = 2 y + ln (y)

lo g_{7} (x + 2) = - 2

What is the answer to ln(x)=1-ln(x+3) ?
The answer to ln(x)=1-ln(x+3) is x=(-3+sqrt(9+4e))/2
Solve for x: ln(x)=1-ln(x+3)
The solution is x=(-3+sqrt(9+4e))/2