Find the sum of the roots of the equation 4^x - 7.2^x + 6 =0

kvishal9956

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The given equation is a quadratic equation in terms of (2^x)^2, so let's make a substitution to simplify it:

Let y = 2^x.

Substituting this into the equation, we get:

(y^2) - (7y) + 6 = 0.

Now, we can solve this quadratic equation for y by factoring or using the quadratic formula:

(y - 6)(y - 1) = 0.

From this, we find two possible values for y:

y = 6, y = 1.

Recalling the substitution, y = 2^x:

2^x = 6, 2^x = 1.

For the equation 2^x = 6, we take the logarithm of both sides to solve for x:

x = log2(6).

For the equation 2^x = 1, we know that any power of 2 equals 1 only when x = 0.

Thus, we have two possible solutions: x = log2(6) and x = 0.

To find the sum of the roots, we add these solutions:

Sum of the roots = log2(6) + 0.
 
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