Question

2^(2+x) - 2^(x+3) + 2^4 = 0

Answer 1

(2+x)÷(x+3)×4=0

(2+x)=0

x=-2

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Answer 2

Answer: x=2

Step-by-step explanation:

Question: 2^(2+x)-2^(x+3)+2^4=0

Step 1: Law of indices: Product law:

Example :( not part of the question)

(3^x) * (3^y)= 3^(x+y)

Therefore, it follows that:

3^(x+y)= (3^x) * (3^y).

Applying the product law to this question:

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

Step 2:

Let (2^x)=y (any letter of your choice)

That is, anywhere you see (2^x) replace it with y;

∴ {(2^2)*y} - {y*(2^3)} + (2^4)=0

Step 3:

• 2^2=2*2=4
• 2^3=2*2*2=8

• 2^4=2*2*2*2=16

∴ {4*y} + {y*8} + 16=0

4y + 8y + 16 =0

Step 4:

Collect like terms by subtracting 8y from 4y which will give us a negative answer (-4y) and by taking 16 to the other side of the equation(making it -16)

-4y=-16

Step 5:

Divide both sides by -4

(-4y)÷(-4)=(-16)÷(-4)

y=4

But this is not our final answer, we are to find the value of x

Step 6:

Referring to Step 2, where we replaced (2^x) with y, now we are replacing y with (2^x)

∴(2^x)=4

Step 7:

4 is also the same as (2^2)

i.e 2*2=4

so, (2^x)=(2^2)

Comparing both sides of the equation, x=2