Question

if 4 to the power x minus 4 to the power x - 1 is equals to 24 then find the value of x​

Answer 1

Answer:

$x =\frac{5}{2}$

Step-by-step explanation:

$4^{x}-4^{x-1}=24$

/* multiply each term by 4 , we get

$4\times 4^{x}-4\times 4^{x-1}=4\times 24$

$\implies 4\times 4^{x}- 4^{1+x-1}=4\times 24$

$Since, \boxed {a^{m}\times a^{n}= a^{m+n}}$

$\implies 4\times 4^{x}- 4^{x}=96$

$\implies 4^{x}(4- 1)=96$

$\implies 4^{x}\times 3 = 96$

$\implies 4^{x}=\frac{96}{3}$

$\implies (2^2)^{x} = 2^{5}$

$\implies (2)^{2x} = 2^{5}$

$\implies 2x =5$

$\implies x =\frac{5}{2}$

Therefore,

$x =\frac{5}{2}$

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