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

The answer to ln(x+4)=2ln(x)+ln(4) is x=(1+sqrt(65))/8

Solve for x: ln(x+4)=2ln(x)+ln(4)

The solution is x=(1+sqrt(65))/8

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

x = \frac{1 + 65}{8}

Decimal Notation

x = 1.13278 \dots

Solution steps

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

Apply log rules

x + 4 = x^{2} \cdot 4

Solve

x + 4 = x^{2} \cdot 4 : x = \frac{1 + 65}{8}, x = \frac{1 - 65}{8}

x = \frac{1 + 65}{8}, x = \frac{1 - 65}{8}

Verify Solutions:

x = \frac{1 + 65}{8}

True

, x = \frac{1 - 65}{8}

False

The solution is

x = \frac{1 + 65}{8}

x^{(l o g_{10} (x))} = 100 x

ln (x) = 5.297293, x

lo g_{10} (x^{2}) = 10

9.3 = - lo g_{10} (x)

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

What is the answer to ln(x+4)=2ln(x)+ln(4) ?
The answer to ln(x+4)=2ln(x)+ln(4) is x=(1+sqrt(65))/8
Solve for x: ln(x+4)=2ln(x)+ln(4)
The solution is x=(1+sqrt(65))/8