Question

find the value of the following ​

Answer 1

Answer:

x = 2 or 3

Step-by-step explanation:

Given equation is

$4^x - 3(2^{x+2}) + 2^5 = 0 \\=> 4^x - 3(2^{x} \times 2^2) + 32 = 0 \\=> 4^x - 3(2^{x} \times 4) + 32 = 0 \\=> 4^x - 12 \times 2^{x} + 32 = 0$

Now , let us assume 2ˣ = t

=> t² - 12t + 32

=> t² - 4t - 8t + 32 = 0

=> t(t-4) - 8(t-4) = 0

=> (t-4)(t-8) = 0

=> t = 4 or t = 8

=> 2ˣ = 4 or 2ˣ = 8

=> x = 2 or x = 3

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Answer 2

Answer:

= 2 or 3

Step-by-step explanation:

Given equation is

\begin{gathered}4^x - 3(2^{x+2}) + 2^5 = 0 \\= > 4^x - 3(2^{x} \times 2^2) + 32 = 0 \\= > 4^x - 3(2^{x} \times 4) + 32 = 0 \\= > 4^x - 12 \times 2^{x} + 32 = 0\end{gathered}

4

x

−3(2

x+2

)+2

5

=0

=>4

x

−3(2

x

×2

2

)+32=0

=>4

x

−3(2

x

×4)+32=0

=>4

x

−12×2

x

+32=0

Now , let us assume 2ˣ = t

=> t² - 12t + 32

=> t² - 4t - 8t + 32 = 0

=> t(t-4) - 8(t-4) =0

(t-4)(t-8) = 0

=> t = 4 or t = 8

=> 2ˣ = 4 or 2ˣ = 8

=> x = 2 or x = 3

Hope it helps

Please mark as brainliest