tkorzhan18 wrote:
KarunMendiratta, can you please explain what approach should be taken to solve this question under time constraint?
This took me less than 90 seconds to solve, hope you can do it too.
\((\frac{4}{10})^{x - 1} = (\frac{625}{100})^{6x - 5}\)
\((\frac{2}{5})^{x - 1} = (\frac{25}{10})^{2(6x - 5)}\)
\((\frac{2}{5})^{x - 1} = (\frac{5}{2})^{12x - 10}\)
\((\frac{2}{5})^{x - 1} = (\frac{2}{5})^{-(12x - 10)}\)
When the bases are equal, the powers are also equal.
i.e. \(x - 1 = -12x + 10\)
\(13x = 11\)
\(x = \frac{11}{13}\)
Now,
Col. A: \((\frac{1}{x})^2\)
Col. B: \(2^x\)
Multipying both sides by \(x^2\);
Col. A: \(1\)
Col. B: \((x^2)(2^x)\)
Col. A: \(1\)
Col. B: \((\frac{11}{13})^2(2^{0.84})\)
Col. A: \(1\)
Col. B: \((\frac{121}{169})(2^{0.84})\)
Col. A: \(1\)
Col. B: \((0.7159)(2^{0.84})\)
We know, \(\sqrt{2} < 2^{0.84} < 2^1\), which means,
Col. A: \(1\)
Col. B: Greater than \(1\)
Hence, option B