Question

2/5^2x+6×2/5^3=2/5^x+2. find the value of x

Answer 1

$\frac{2}{5} ^{2x + 6} * \frac{2}{5} ^{3} = \frac{2}{5} ^{x +2}$

Now,
2/5 ^2x + 6 + 3 = 2/5 ^x+2
2/5 ^2x + 9 = 2/5 ^x+2
∵As the bases are equal so the powers are also equal.
∴2x + 9 = x + 2
∴2x - x = 2 - 9
∴ x = -7.

Answer 2

$Hi \: \: !!! \\ \\ Here \: \: is \: \: your \: \: answer, \\ \\ {( \frac{2}{5}) }^{2x + 6} \times {( \frac{2}{5} )}^{3} = { (\frac{2}{5} )}^{x + 2} \\ \\ = > ( { \frac{2}{5} )}^{2x + 6 + 3} = { (\frac{2}{5} )}^{x + 2} \\ \\ = > ( { \frac{2}{5} )}^{2x + 9} = { (\frac{2}{5} )}^{x + 2} \\ Bases \: \: are \: \: same \: \\ now \: \: equating \: \: their \: \: powers \\ = > 2x + 9 = x + 2 \\ = > 2x - x = 2 - 9 \\ = > x = - 7 \\ \\ \\ Verification \\ (L.H.S) \\ {( \frac{2}{5} )}^{2x + 6} \times ({ \frac{2}{5} )}^{3} \\ \\ = {( \frac{2}{5} )}^{2x + 6 + 3 } \\ \\ = {( \frac{2}{5} )}^{2x + 9} \\ \\ = {( \frac{2}{5} )}^{2 \times ( - 7) + 9} \\ \\ = {( \frac{2}{5}) }^{ - 14 + 9} \\ \\ = {( \frac{2}{5} )}^{ - 5} \\ \\ \\ (R.H.S) \\ {( \frac{2}{5} )}^{x + 2} \\ \\ = {( \frac{2}{5} })^{ \: - 7 + 2} \\ \\ = {( \frac{2}{5}) }^{ - 5} \\ \\ \\ Hence, \\ L.H.S = R.H.S \\ \\ \\ Hope \: \: it \: \: helps.$