Question

find the value of 2^x​

Answer 1

Answer:

${2}^{x + y} = 10 ....(1) \\ {2}^{y + z} = 20....(2) \\ {2}^{z + x} = 30....(3) \\ from \: equation \: (2) \\ {2}^{y + z} = 20 \implies \: {2}^{y + z} = 2 \times 10 \\ \implies \: {2}^{y + z} = 2 \times {2}^{x + y}\\... [from\: equation \:(1)] \\ \implies \: {2}^{y + z} = {2}^{x + y + 1} \\ \implies y + z = x + y + 1\\ \implies \huge \fbox {z = x + \: 1} \\ from \: equation \: (3) \\ {2}^{z + x} = 30 \\ \implies \: {2}^{x + 1+ x} = 30\\ \implies \: {2}^{2x + 1} = 30\\ \implies \: {2}^{2x} \times {2}^{1} = 30\\ \implies \: {2}^{2x} \times 2 = 30\\ \implies \: {2}^{2x} = \frac{30}{2} \\ \implies \: {2}^{2x} = 15\\ \implies \: ({2}^{x})^{2} = 15 \\ \implies \: \huge \fbox{{2}^{x} = \sqrt{15} }$

Thus, option (2) is the correct answer.