Question

3a/2b 2x-4 = 2b/3a 2x-4

Answer 1

Answer:

${( \frac{3a}{2b}) }^{2x - 4} = {( \frac{2b}{3a}) }^{2x - 4} \\ {( \frac{3a}{2b}) }^{2x - 4} = {( \frac{3a}{2b}) }^{ - (2x - 4)}$

Identity used:

${a}^{ - m} = \frac{1}{ {a}^{ - m} } \: (or) \: { ( \frac{a}{b} )}^{ - m } = { (\frac{b}{a}) }^{m}$

Now, as the bases are equal, equating the powers of the bases.

$2x - 4 = - (2x - 4) \\ 2x - 4 = - 2x + 4 \: \: \: \\ 2x + 2x = 4 + 4 \: \: \: \: \: \: \: \: \: \: \: \: \\ 4x = 8 \: \: \: \: \: \: \: \: \: \\ x = \frac{8}{4} \: \: \: \: \: \\ x = 2 \: \: \: \: \: \:$

Therefore, the value of x is 2.