Question

If$\underset{x\to c}{\lim }\ln \left(f\right(x\left)\right)=L$, then$\underset{x\to c}{\lim }f\left(x\right)=\_\_\_\_$.

Short answer

If$\underset{x\to c}{\lim }\ln \left(f\right(x\left)\right)=L$, thenlocalid="1648558625386" $\underset{x\to c}{\lim }f\left(x\right)=e^L$.

Step-by-step solution

Step 1. Given information 

The given statement is,

If$\underset{x\to c}{\lim }\ln \left(f\right(x\left)\right)=L$, thenlocalid="1648558733203" role="math" $\underset{x\to c}{\lim }f\left(x\right)=\_\_\_\_$.

Step 2. Fill in the blanks  

The given statement is a theorem

That is,

If$\underset{x\to c}{\lim }\ln \left(f\right(x\left)\right)=L$, thenlocalid="1648558702618" $\underset{x\to c}{\lim }f\left(x\right)=e^L$.