What is the answer to 2ln(x-3)+ln(x+9)=3ln(x) ?

The answer to 2ln(x-3)+ln(x+9)=3ln(x) is x=(3(5+sqrt(13)))/2

Solve for x: 2ln(x-3)+ln(x+9)=3ln(x)

The solution is x=(3(5+sqrt(13)))/2

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2 ln (x - 3) + ln (x + 9) = 3 ln (x)

x = \frac{3 ( 5 + 13 )}{2}

Decimal Notation

x = 12.90832 \dots

Solution steps

2 ln (x - 3) + ln (x + 9) = 3 ln (x)

Apply log rules

(x - 3)^{2} (x + 9) = x^{3}

Solve

(x - 3)^{2} (x + 9) = x^{3} : x = \frac{3 ( 5 + 13 )}{2}, x = \frac{3 ( 5 - 13 )}{2}

x = \frac{3 ( 5 + 13 )}{2}, x = \frac{3 ( 5 - 13 )}{2}

Verify Solutions:

x = \frac{3 ( 5 + 13 )}{2}

True

, x = \frac{3 ( 5 - 13 )}{2}

False

The solution is

x = \frac{3 ( 5 + 13 )}{2}

0 = lo g_{10} (x + 1)

9 lo g_{x} (3) = lo g_{3} (x)

lo g_{4} (x - 2) - lo g_{4} (x - 4) = 2

lo g_{10} (\frac{1}{x}) = - 5.37

ln (3 x - 19) = 3

What is the answer to 2ln(x-3)+ln(x+9)=3ln(x) ?
The answer to 2ln(x-3)+ln(x+9)=3ln(x) is x=(3(5+sqrt(13)))/2
Solve for x: 2ln(x-3)+ln(x+9)=3ln(x)
The solution is x=(3(5+sqrt(13)))/2