Question

Find the value of $x$ in ${\left(\frac{11}{12}\right)}^x÷{\left(\frac{12}{11}\right)}^5={\left(\frac{11}{12}\right)}^{10}$

• A. $5$
• B. $-5$
• C. $4$
• D. $0$

Answer 1

The correct option is A $5$

Consider, ${\left(\frac{11}{12}\right)}^x÷{\left(\frac{12}{11}\right)}^5={\left(\frac{11}{12}\right)}^x\times {\left(\frac{11}{12}\right)}^5$
$={\left(\frac{11}{12}\right)}^{x+5}$
Given, ${\left(\frac{11}{12}\right)}^{x+5}={\left(\frac{11}{12}\right)}^{10}$
$\therefore x+5=10$
$\therefore x=5$