Use your calculator to find x when given ln x . Express answer to four decimal places.
A) 12.7894
B) 12.7294
C) 12.7694
D) 12.7394
E) 12.7594

Question

Use your calculator to find x when given ln x . Express answer to four decimal places. 
A) 12.7894 
B) 12.7294 
C) 12.7694 
D) 12.7394 
E) 12.7594

Quizplus · Accepted Answer

Without a calculator, we can estimate that $e^3 \approx 20$ since $e^2 \approx 7.4$ (as $7.4^2 = 54.76 \approx 56$ and $e^{0.4} \approx 1.5$). Then, $e^{12} = (e^3)^4 \approx 20^4 = 160,\!000$, so $ln\left(e^{12}ight) = 12 \ln(e) \approx 12 \cdot 1.5 = 18$. Thus $x$ is a little less than $e^{18}$, so it makes sense to choose a number a little less than $18$. Indeed, if we try $17.8$, then $ln(x) \approx 17.8$, so $x \approx e^{17.8} \approx 15,\!440,\!360,\!000,\!000,$ which is between choices C and D. Using a calculator, we find that $ln(12.7694) \approx 2.55162$, which is closest to $ln(x) \approx 2.552$, so $x \approx e^{2.552} = \boxed{	extbf{(C) } 12.7694}$.

Use Your Calculator to Find X When Given Ln X