Question

4 raise to power x minus 4 raise to power x minus 1 is equal to 24 find the value of x

Answer 1

$$\begin{gathered} Dearstudent, \\ {4}^x-4^{x-1}=24 \\ {4}^x-4^x\times 4^{-1}=24 \\ {4}^x(1-4^{-1})=24 \\ {4}^x(1-\frac{1}{4})=24 \\ takingLCM \\ {4}^x\times \frac{3}{4}=24 \\ {4}^x=24\times \frac{4}{3} \\ {4}^x=8\times 4 \\ {4}^x=32 \\ (2^2{)}^x=2^5 \\ {2}^{2x}=2^5 \\ Asthebasesaresame, \\ weequatethepowers, \\ therefore2x=5 \\ x=\frac{5}{2} \\ Regards \end{gathered}$$