Question

If 5^x+1=25^x-2 ; find the value of : 3^x-3 × 2^3-x

Answer 1

${5}^{(x + 1)} = {25}^{(x - 2)} \\ \\ {5}^{(x + 1)} = {5}^{2(x - 2)} \\ \\ {5}^{(x + 1)} = {5}^{(2x - 4)} \\ \\ x + 1 = 2x - 4 \\ \\ x = 5$

Now,

${3}^{(x - 3)} \times {2}^{(3 - x)} = {3}^{(5 - 3)} \times {2}^{(3 - 5)} \\ \\ = {3}^{2} \times {3}^{ - 2} \\ \\ = {3}^{(2 - 2)} \\ \\ = {3}^{0} \\ \\ = 1$