Solve the following equations for $x$:
$ 2^{2 x}-2^{x+3}+2^{4}=0 $

Given:

\( 2^{2 x}-2^{x+3}+2^{4}=0 \)

To do:

We have to find the value of $x$.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$  

Therefore,

$2^{2 x}-2^{x+3}+2^{4}=0$

$(2^x)^{2}-2^x \times(2)^{3}+(2^2)^{2}=0$

$(2^x)^{2}-2\times 2^x \times(2^{2})+(2^2)^{2}=0$

$(2^x-2^2)^2=0$                                  [Since $a^2-2ab+b^2=(a-b)^2$]

$\Rightarrow 2^x-4=0$

$\Rightarrow 2^x=4$

$\Rightarrow 2^x=2^2$

Comparing the powers on both sides, we get,

$x=2$

Therefore, the value of $x$ is $2$.  

Tutorialspoint

Updated on: 10-Oct-2022

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