Question

Solve the equation:

1-2 lnx = -4
~ [?]
X~
Round your answer to the nearest thousandth.

Answer 1

x ≈ 12.182

Explanation:

1 - 2lnx = - 4 ( subtract 1 from both sides )

- 2lnx = - 5 ( divide both sides by - 2 )

lnx = 2.5

x =
`e^(2.5)` ≈ 12.182 ( to the nearest thousandth )

Answer 2

x = 12.182 (nearest thousandth)

Explanation:

Given equation:

`1-2 \ln x=-4`

Subtract 1 from both sides:

`\implies 1-1 -2 \ln x =-4-1`

`\implies -2 \ln x=-5`

Divide both sides by -2:

`\implies (-2 \ln x)/(-2)=(-5)/(-2)`

`\implies \ln x = (5)/(2)`

`\textsf{As }\: \ln x=\log_ex \:\:\textsf{}`, the natural logarithm can be canceled by giving both sides a base of e (Euler's number):

`\implies e^(\ln x)= e^{(5)/(2)`

`\implies x= e^{(5)/(2)`

`\implies x=12.182\:\: \sf (nearest\:thousandth)`