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Solve for x if 1 equals first part of equation 100 divided by 2 to the power of 2x plus second part of equation 10 divided by 2 to the power of x?
Wiki User
∙ 11y ago
The first part of the equation is the square of the second part, since 100 is 10 squared and the square of 2x is 22x. Writing y for 10/2x, we get the quadratic equation y2 + y = 1. Using the quadratic formula, we get y = (-1 + or - square root of 5)/2. Since real powers of 2 are all positive, we take the positive square root. Substituting for y and solving for x, we get x = log2(20/((square root of 5)-1)). You can calculate the value of this by using a scientific calculator, using the fact that log of a number to the base 2 is the natural log of the number divided by the natural log of 2. I get about 4.016.
Wiki User
∙ 11y ago
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