Question

$\underset{x\to 0}{lim}\left(\frac{3^x-1}{x}\right)$ is equal to

• A. $2\log 3$
• B. $3\log 3$
• C. $\log 3$
• D. None of these

Answer 1

Answer: (C)

$\log 3$

$\underset{x\to 0}{lim}\left(\frac{3^x-1}{x}\right)\left(\frac{0}{0}\text{form}\right)$

Using L' Hospital's rule

$=\underset{x\to 0}{lim}\frac{3^x\log 3-0}{1}=3^0\log 3$

$=\log 3$