What is the answer to 2ln(x-3)+ln(x+8)=3ln(x) ?

The answer to 2ln(x-3)+ln(x+8)=3ln(x) is x=(39+3sqrt(105))/4

Solve for x: 2ln(x-3)+ln(x+8)=3ln(x)

The solution is x=(39+3sqrt(105))/4

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2 ln (x - 3) + ln (x + 8) = 3 ln (x)

x = \frac{39 + 3 105}{4}

Decimal Notation

x = 17.43521 \dots

Solution steps

2 ln (x - 3) + ln (x + 8) = 3 ln (x)

Apply log rules

(x - 3)^{2} (x + 8) = x^{3}

Solve

(x - 3)^{2} (x + 8) = x^{3} : x = \frac{39 + 3 105}{4}, x = \frac{39 - 3 105}{4}

x = \frac{39 + 3 105}{4}, x = \frac{39 - 3 105}{4}

Verify Solutions:

x = \frac{39 + 3 105}{4}

True

, x = \frac{39 - 3 105}{4}

False

The solution is

x = \frac{39 + 3 105}{4}

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

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

lo g_{b} (3) = \frac{1}{4}

n lo g_{10} (n) = 3.6 \cdot 1 0^{13}

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

What is the answer to 2ln(x-3)+ln(x+8)=3ln(x) ?
The answer to 2ln(x-3)+ln(x+8)=3ln(x) is x=(39+3sqrt(105))/4
Solve for x: 2ln(x-3)+ln(x+8)=3ln(x)
The solution is x=(39+3sqrt(105))/4