Answer:
To solve the equation 2^(2x) - 2^x = 2^3, we can rewrite it using a substitution. Let's substitute y = 2^x:
Substituting y = 2^x, the equation becomes:
y^2 - y = 2^3
Now, we have a quadratic equation in terms of y. Let's rearrange it:
y^2 - y - 8 = 0
To solve this quadratic equation, we can factor it:
(y - 4)(y + 2) = 0
Setting each factor equal to zero, we have two possible solutions:
y - 4 = 0 --> y = 4
y + 2 = 0 --> y = -2
Now, let's substitute back y = 2^x:
For y = 4:
2^x = 4
Taking the logarithm base 2 of both sides:
x = log2(4)
x = 2
For y = -2:
2^x = -2
There is no real solution for this case since 2^x is always positive.
Therefore, the solution to the equation 2^(2x) - 2^x = 2^3 is x = 2.
Step-by-step explanation:
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thankyou ttg Robin this question is wrong because what do you mean by it??
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Verified answer
Answer:
To solve the equation 2^(2x) - 2^x = 2^3, we can rewrite it using a substitution. Let's substitute y = 2^x:
Substituting y = 2^x, the equation becomes:
y^2 - y = 2^3
Now, we have a quadratic equation in terms of y. Let's rearrange it:
y^2 - y - 8 = 0
To solve this quadratic equation, we can factor it:
(y - 4)(y + 2) = 0
Setting each factor equal to zero, we have two possible solutions:
y - 4 = 0 --> y = 4
y + 2 = 0 --> y = -2
Now, let's substitute back y = 2^x:
For y = 4:
2^x = 4
Taking the logarithm base 2 of both sides:
x = log2(4)
x = 2
For y = -2:
2^x = -2
There is no real solution for this case since 2^x is always positive.
Therefore, the solution to the equation 2^(2x) - 2^x = 2^3 is x = 2.
Step-by-step explanation:
pls mark me brainliest please
thankyou ttg Robin this question is wrong because what do you mean by it??