What is the answer to -1000ln(1+x^2)+6000=2000 ?

The answer to -1000ln(1+x^2)+6000=2000 is x=sqrt(e^4-1),x=-sqrt(e^4-1)

Solve for x: -1000ln(1+x^2)+6000=2000

The solution is x=sqrt(e^4-1),x=-sqrt(e^4-1)

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- 1000 ln (1 + x^{2}) + 6000 = 2000

x = e^{4} - 1, x = - e^{4} - 1

Decimal Notation

x = 7.32107 \dots, x = - 7.32107 \dots

Solution steps

- 1000 ln (1 + x^{2}) + 6000 = 2000

Move

6000

to the right side

- 1000 ln (1 + x^{2}) = - 4000

Divide both sides by

- 1000

ln (1 + x^{2}) = 4

Apply log rules

1 + x^{2} = e^{4}

Solve

1 + x^{2} = e^{4} : x = e^{4} - 1, x = - e^{4} - 1

x = e^{4} - 1, x = - e^{4} - 1

Verify Solutions:

x = e^{4} - 1

True

, x = - e^{4} - 1

True

The solutions are

x = e^{4} - 1, x = - e^{4} - 1

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

lo g_{2} ((m - 6) (m + 1)) = 3

lo g_{10} (x^{2} + 1) = - 0.7

5.56 = ln (\frac{x}{100})

lo g_{10} (x - 2) = \frac{11}{5}

What is the answer to -1000ln(1+x^2)+6000=2000 ?
The answer to -1000ln(1+x^2)+6000=2000 is x=sqrt(e^4-1),x=-sqrt(e^4-1)
Solve for x: -1000ln(1+x^2)+6000=2000
The solution is x=sqrt(e^4-1),x=-sqrt(e^4-1)