Question

Solve the equation:

Answer 1

Answer:

x = 12.182  (nearest thousandth)

Step-by-step 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:

$\implies \dfrac{-2 \ln x}{-2}=\dfrac{-5}{-2}$

$\implies \ln x = \dfrac{5}{2}$

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

$\implies e^{\ln x}= e^{\frac{5}{2}$

$\implies x= e^{\frac{5}{2}$

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

Answer 2

Answer:

x ≈ 12.182

Step-by-step 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 )