VIDEO: Resolving e to the power of x

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So you can solve e to the power of x

When calculating exponential growth or exponential decay, the exponential function, usually also called the exponential function, is used

  • If you are with such Functions To do the math, you must also use an equation of the form e to the power of x = number, mathematically more precisely: ex = a, solve for the unknown x.
  • A simple trick helps to get to the unknown "x": You form the natural logarithm ln on both sides of the equation. As a reminder: The logarithm, regardless of the base, is always a question of the exponent - in this case the "x" that you want to calculate.
  • If this arithmetic operation seems strange to you at first, you should remind yourself how you solve quadratic equations (i.e. x² = a). There you simply form the opposite operation to squaring, namely the extraction of the roots. It is the same with equations of the form ex. The natural logarithm is here the opposite operation to the exponential function.

If the exponential equation you are supposed to solve is not in the form "e to the power of x", then you must first use the power laws to bring the equation to this form. Only then is the natural logarithm applied.

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Simple example of exponential equations

The procedure is to be explained using a simple example. Given the equation e to the power of x = 2, mathematically formulated ex = 2, which you should solve for x. Such Equations often arise when calculating half-lives or growth times.

  1. First, form the natural logarithm on both sides of the equation: ln (ex) = ln 2.
  2. Now ln (ex) = x. This step becomes clear because one knows that "ln" and "e high" are counter-operations, that is to say, to put it casually, "cancel each other out". You can also use the logarithmic laws and get ln (ex) = x * ln e = x, since ln e = 1.
  3. So you get x = ln 2.
  4. Now all you really need is yours calculator (or a log table) to calculate ln 2.

Should the equation e2x-2 = 15 are solved, is also logarithmized. This results in 2x-2 = ln 15. You can easily solve this equation.

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