Question

$\underset{x\to 0}{lim}\frac{4^x-1}{3^x-1}$ equals

• A. ${\log }_{3}4$
• B. ${\log }_{4}3$
• C. $\log \frac{4}{3}$
• D. $1$

Answer 1

The correct option is A ${\log }_{3}4$

Given, $\underset{x\to 0}{lim}\frac{4^x-1}{3^x-1}=\underset{x\to 0}{lim}\frac{4^x\log 4-0}{3^x\log 3-0}$ [using L'Hospital's rule]
$=\frac{\log 4}{\log 3}$
$={\log }_{3}4$