VIDEO: Solve 2 to the power of x for x

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Solve the equation for x - that's how it works

Simple Equations, in which the x occurs only in the first power, are relatively easy to solve. To do this, simply combine all the links that contain an x ​​and bring them on the same side. Bring everything else to the other side of the equal sign and you can simply solve for x.

  • Do you have e.g. B. given the equation 2x-3 = 6x + 4, then first subtract 2x on both sides, then subtract 4 on both sides and finally divide by 4 in the last step. The result is 2x-3 = 6x + 4 equivalent -3 = 4x + 4, so -7 = 4x and finally x = -7/4.
  • In principle, you proceed in the same way with a quadratic equation. In addition, they also combine all the square links. Transform the term into the form 0 = ax2+ bx + c then you can apply the midnight formula and x1/2 to calculate.
  • But what do you do when the x appears in the exponent, for example at 2 to the power of x? To do this, look at the simple equation 2x = 3 on.

Resolving 2 to the power of x 

  1. If you have 2 to the power of x, you need to know that f (x) = 2 x with x from the real Counting is an exponential function. If you have such a kind of equation, it is not that easy to solve for x.
    2. Reverse the logarithm - that's how it works

    The inverse function of the logarithm is not difficult to determine. You have to ...

  2. As with everyone else Functions it is now particularly easy for you to work with the inverse function. For example, you use the arcsine for a sine term and the root for a quadratic expression. For an exponential function, the inverse function is the logarithm.
  3. Which logarithm you use is up to you. For example, you can work with the natural logarithm. Now solve equation 2x = 3 to x by using the natural logarithm on both sides. Then apply the third law of the logarithm lg (a)b = b * lg (a) an.
  4. It results in 2x = 3 is equivalent to ln (2x) = ln (3), this results in x * ln (2) = ln (3) and finally x = ln (3) / ln (2).

It is best to do this exercise with two or three other simple equations that have an x ​​in the exponent.

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