GATE2017 CE-2: GA-4

Question

What is the value of $x$ when $81\times\left (\frac{16}{25} \right )^{x+2}\div\left (\frac{3}{5} \right )^{2x+4}=144?$

• A. $1$
• B. $-1$
• C. $-2$
• D. $\text{Can not be determined}$

Comments

Easiest way is to substitute value,

If you try to smiplify it you may end up something like $(\frac{16}{9})$ $^{x+1}$ = 1 , only -1 stastify

Answer 1

$\text{By Prime Factorization,the given equation can be written as}$

$$ 3^4 \times \frac {2^{4x+8}}{5^{2x+4}} \times \frac {3^{-2x-4}}{5^{-2x-4}} = 3^2\times 2^4$$

$\text{comparing the powers of 2 on both sides}$

$$ \text{4x+8 = 4 }\implies x = -1$$

$$\text{(OR)}$$

$\text{comparing the powers of 3 on both sides}$

$$ \text{4-2x-4 = 2 }\implies x = -1$$