Question

${2}^{x + 2} + {2}^{x - 1} = 9$
find value of x
​

Answer 1

Answer:

x=2

Step-by-step explanation:

${2}^{x + 2} + {2}^{x - 1} = 9 \\( {2}^{x} \times {2}^{2}) + ( {2}^{x} \times {2}^{ - 1} ) = 9 \\ {2}^{x} ( {2}^{2} + {2}^{ - 1} ) = 9 \\ {2}^{x} (4 + \frac{1}{2} ) = 9 \\ {2}^{x} ( \frac{9}{4} ) = 9 \\ {2}^{x} = \frac{9}{ \frac{9}{4} } \\ {2}^{x} = 9 \times \frac{4}{9} \\ {2}^{x} =4 \\ {2}^{x} = {2}^{2} \\ x = 2$