What is the answer to ln(4x)-3ln(x^2)=ln^2(x) ?

The answer to ln(4x)-3ln(x^2)=ln^2(x) is x=e^{(-5+sqrt(25+8ln(2)))/2},x=e^{(-5-sqrt(25+8ln(2)))/2}

Solve for x: ln(4x)-3ln(x^2)=ln^2(x)

The solution is x=e^{(-5+sqrt(25+8ln(2)))/2},x=e^{(-5-sqrt(25+8ln(2)))/2}

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ln (4 x) - 3 ln (x^{2}) = ln^{2} (x)

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

Decimal Notation

x = 1.30132 \dots, x = 0.00517 \dots

Solution steps

ln (4 x) - 3 ln (x^{2}) = ln^{2} (x)

Apply log rules

ln (4) + ln (x) - 3 \cdot 2 ln (x) = ln^{2} (x)

Rewrite the equation with

ln (x) = u

ln (4) + u - 3 \cdot 2 u = u^{2}

Solve

ln (4) + u - 3 \cdot 2 u = u^{2} : u = \frac{- 5 + 25 + 8 ln ( 2 )}{2}, u = \frac{- 5 - 25 + 8 ln ( 2 )}{2}

u = \frac{- 5 + 25 + 8 ln ( 2 )}{2}, u = \frac{- 5 - 25 + 8 ln ( 2 )}{2}

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = \frac{- 5 + 25 + 8 ln ( 2 )}{2} : x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}

Solve

ln (x) = \frac{- 5 - 25 + 8 ln ( 2 )}{2} : x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

Verify Solutions:

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}

True

, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

True

The solutions are

x = e^{\frac{- 5 + 25 + 8 l n ( 2 )}{2}}, x = e^{\frac{- 5 - 25 + 8 l n ( 2 )}{2}}

(ln (x))^{3} = 7 ln (x)

lo g_{4} (100 - 3 x) = 23219

6 = lo g_{10} (x)

x, - 5 lo g_{3} (2 x) = - 5

1 + lo g_{\frac{1}{2}} (x) = 0

What is the answer to ln(4x)-3ln(x^2)=ln^2(x) ?
The answer to ln(4x)-3ln(x^2)=ln^2(x) is x=e^{(-5+sqrt(25+8ln(2)))/2},x=e^{(-5-sqrt(25+8ln(2)))/2}
Solve for x: ln(4x)-3ln(x^2)=ln^2(x)
The solution is x=e^{(-5+sqrt(25+8ln(2)))/2},x=e^{(-5-sqrt(25+8ln(2)))/2}