Question

Evaluate the logarithm

Answer 1

Question:

• 
  `ln\frac{1}{\sqrt{e^(3)}}=x`

To find :

• Value of x

solution:

`ln\frac{1}{\sqrt{e^(3)}}=x\\\\ e^{^{({ln\frac{1}{\sqrt{e^(3)}}})}}=e^(x)\\\\ \frac{1}{\sqrt{e^(3)}}=e^(x) \\\\ (\frac{1}{\sqrt{e^(3)}})^(2)=e^(2x)\\\\ (1)/(e^(3))=e^(2x)\\\\ e^(-3)=e^(2x)\\\\ -3=2x \\\\\sf{x=(-3)/(2)}`

final answer:

• 
  `\pmb{(-3)/(2)}`