Question

solve for x.6-2ln x = 7Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

In order to solve the given equation, we can apply a series of the same operations on both sides of the equation, until we isolate the variable x and find its value:

`\begin{gathered} 6-2\ln x=7 \\ \\ 6-2\ln x-6=7-6 \\ \\ -2\ln x=1 \\ \\ \ln x=-(1)/(2) \\ \\ e^(\ln x)=e^{-(1)/(2)} \\ \\ x=e^{-(1)/(2)}=\frac{1}{e^{(1)/(2)}}=\frac{1}{\sqrt[]{e}^{}} \end{gathered}`

Now, computing this value, and rounding to the nearest hundredth, we find:

`x\cong0.61`