Question 91

If $$9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$, then $$x$$ is


It is given that $$9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$$

Let us try to reduce them to powers of $$3$$ and $$2$$
The given equation can be reduced to $$3^{2x-1} + 3^{2x-3} = 2^{2x} + 2^{2x-2}$$

Hence, $$3^{2x-3} \times 10 = 2^{2x-2} \times 5$$
Therefore, $$3^{2x-3} = 2^{2x-3}$$

This is possible only if $$2x-3=0$$ or $$x=3/2$$

Video Solution


Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 35+ CAT previous papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free


Boost your Prep!

Download App