Question

If 4^x+1-4^x=24, what is the value of (2x)^x​

Answer 1

${\huge{\purple{\underbrace{\text{\red{Solution }}}}}}$

$\begin{gathered} {4}^{x} - {4}^{x - 1} = 24 \\ {4}^{x} - {4}^{x} \times {4}^{ - 1} = 24 \\ {4}^{x} (1 - \frac{1}{4}) = 24 \\ {4}^{x} \times \frac{3}{4} = 24 \\ {4}^{x} = 24 \times \frac{4}{3} \\ {4}^{x} = 8 \times4 \\ {2}^{2x} = 32 \\ {2}^{2x} = {2}^{5} \\ 2x = 5 \\ x = \frac{5}{2} \\ (2x) ^{x} = (2 \times \frac{5}{2} )^{ \frac{5}{2} } = 5^{ \frac{5}{2} } \: \end{gathered}$