What is the answer to ln(3)-ln(x+5)-ln(x)=0 ?

The answer to ln(3)-ln(x+5)-ln(x)=0 is x=(-5+sqrt(37))/2

Solve for x: ln(3)-ln(x+5)-ln(x)=0

The solution is x=(-5+sqrt(37))/2

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ln (3) - ln (x + 5) - ln (x) = 0

x = \frac{- 5 + 37}{2}

Decimal Notation

x = 0.54138 \dots

Solution steps

ln (3) - ln (x + 5) - ln (x) = 0

Add

ln (x + 5)

to both sides

ln (3) - ln (x + 5) - ln (x) + ln (x + 5) = 0 + ln (x + 5)

Simplify

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

Add

ln (x)

to both sides

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

Simplify

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

Apply log rules

3 = (x + 5) x

Solve

3 = (x + 5) x : x = \frac{- 5 + 37}{2}, x = \frac{- 5 - 37}{2}

x = \frac{- 5 + 37}{2}, x = \frac{- 5 - 37}{2}

Verify Solutions:

x = \frac{- 5 + 37}{2}

True

, x = \frac{- 5 - 37}{2}

False

The solution is

x = \frac{- 5 + 37}{2}

lo g_{x} (\frac{1}{4}) = - 1

ln (- x) = 0

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

lo g_{3} ((r + 6)^{2}) = 4

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

What is the answer to ln(3)-ln(x+5)-ln(x)=0 ?
The answer to ln(3)-ln(x+5)-ln(x)=0 is x=(-5+sqrt(37))/2
Solve for x: ln(3)-ln(x+5)-ln(x)=0
The solution is x=(-5+sqrt(37))/2