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 Notation

x = 3.72896 \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}

2 ln (x) - ln (x + 5) = ln (x) - ln (3)

2 ln (x) - ln (x - 1) = ln (4)

3.5 = 1.5 + lo g_{3} (x + 1)

lo g_{10} (3 x) = 4

lo g_{3} (y^{2}) + lo g_{3} (y) = 6

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