What is the answer to 2ln(x)-2ln(x+2)=4ln(x^2) ?

The answer to 2ln(x)-2ln(x+2)=4ln(x^2) is x\approx 0.71667…

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2ln(x)-2ln(x+2)=4ln(x^2)

2 ln (x) - 2 ln (x + 2) = 4 ln (x^{2})

x \approx 0.71667 \dots

Solution steps

2 ln (x) - 2 ln (x + 2) = 4 ln (x^{2})

Divide both sides by

2

\frac{2 ln ( x )}{2} - \frac{2 ln ( x + 2 )}{2} = \frac{4 ln ( x ^{2} )}{2}

Simplify

ln (x) - ln (x + 2) = 2 ln (x^{2})

Add

ln (x + 2)

to both sides

ln (x) - ln (x + 2) + ln (x + 2) = 2 ln (x^{2}) + ln (x + 2)

Simplify

ln (x) = 2 ln (x^{2}) + ln (x + 2)

Apply log rules

x = x^{4} (x + 2)

Solve

x = x^{4} (x + 2) : x = 0, x \approx 0.71667 \dots, x \approx - 2.10691 \dots

x = 0, x \approx 0.71667 \dots, x \approx - 2.10691 \dots

Verify Solutions:

x = 0

False

, x \approx 0.71667 \dots

True

, x \approx - 2.10691 \dots

False

The solution is

x \approx 0.71667 \dots

ln (x^{2} - x - 1) = 0

lo g_{3} (2 x^{2} + 5 x + 4) - 7 = 2

\frac{lo g _{10} ( 6 - x ^{2} )}{lo g _{10} ( 3 x - 4 )} = 2

lo g_{4} (x + 12) - lo g_{4} (5 - x) = 2

lo g_{2} (x + 7) = 5

What is the answer to 2ln(x)-2ln(x+2)=4ln(x^2) ?
The answer to 2ln(x)-2ln(x+2)=4ln(x^2) is x\approx 0.71667…
Solve for x: 2ln(x)-2ln(x+2)=4ln(x^2)
The solution is x\approx 0.71667…