Question

Find the value of $x$ in: ${\left(\frac{12}{13}\right)}^{3x}÷{\left(\frac{13}{12}\right)}^4={\left(\frac{12}{13}\right)}^{10}$

• A. $2$
• B. $3$
• C. $4$
• D. $-2$

Answer 1

The correct option is A $2$

LHS $={\left(\frac{12}{13}\right)}^{3x}÷{\left(\frac{13}{12}\right)}^4$

$={\left(\frac{12}{13}\right)}^{3x}\times {\left(\frac{12}{13}\right)}^4$ $={\left(\frac{12}{13}\right)}^{3x+4}$

Now, ${\left(\frac{12}{13}\right)}^{3x+4}={\left(\frac{12}{13}\right)}^{10}$

$\therefore 3x+4=10$
$\therefore 3x=6$
$\therefore x=2$

So, option $A$ is correct.