​$$\text{If } 2^x - 2^{x-1} = 32,\ \text{then the value of } \frac{2x - 1}{2x + 3} \text{ is:}$$​​

Correct option is C

Given:

$$2^x - 2^{x-1} = 32 \\ \ \\\frac{2x-1}{2x+3} =?$$​

Solution:

​$$2^x - 2^{x-1} = 32$$​​

​$$2^{x-1}(2 -1 ) = 32$$​​

​$$2^{x-1} = 2^5$$​​

Comparing powers,

x - 1 = 5

x = 6

​$$\frac{2x - 1}{2x + 3} = \frac{2(6) - 1}{2(6) + 3} = \frac{12 - 1}{12 + 3} = \frac{11}{15}$$