Question

3. Solve for x as
(4^x)-(4^x-1)-(4^x-2) = 22​

Answer 1

$\large\underline\purple{\bold{Solution :- }}$

$\tt \ \: :  ⟼ {4}^{x} - {4}^{x - 1} - {4}^{x - 2} = 22$

$\tt \ \: :  ⟼ {4}^{x} - \dfrac{ {4}^{x} }{4} - \dfrac{ {4}^{x} }{ {4}^{2} } = 22$

$\tt \ \: :  ⟼ {4}^{x} (1 - \dfrac{1}{4} - \dfrac{1}{16} ) = 22$

$\tt \ \: :  ⟼ {4}^{x} (\dfrac{16 - 4 - 1}{16} )= 22$

$\tt \ \: :  ⟼ {4}^{x} \times \dfrac{11}{16} = 22$

$\tt\implies \: {4}^{x} = 32$

$\tt\implies \: {2}^{2x} = {2}^{5}$

$\tt\implies \:x = \dfrac{5}{2}$