Question

Lnx=-3

the answer in the textbook says it becomes x=e^-3 which I agree with, but then it gives 0.05 as the answer to solving it, I just don't understand how they found 0.05. Can anyone explain how to get 0.05 from x=e^-3?

Answer 1

because It's rounded to the nearest hundred place

Explanation:

Given equation:

• 
  `\ln(x ) = - 3`

recall that,

`\ln(a ) = b \iff {e}^(b) = a`

remember, In is natural logarithm which is actually nothing but common logarithm with the base euler's number (e) . anyway rewriting lnx=-3 yields:

`\ln( x ) = - 3\\ \iff {e}^( - 3) = \frac{1}{ {e}^(3) }`

1/e³ is approximately 0.0497870684..... , rounding it to the nearest hundred place would be 0.05 which is the same answer as your textbook .