Exponential Equations

Exponential Equations
An exponential equation is one that has exponential expressions, in other words, powers that have in their exponent expressions with the unknown factor x. For example:
We will resolve some exponential equations without using logarithms. This method of resolution consists in reaching an equality of the exponentials with the same base in order to equal the exponents.
Examples
Example 1:
Taking into account that we can write 16 as a power
we can rewrite the equation as
Therefore,
So, the solution is x = 2.
Example 2:
Taking into account that
We can rewrite the equation as
This way, we can extract a common factor of 2 x:
Therefore, the solution is
Example 3:
Taking into account that
We can rewrite the equation as
We have the common base 3 x, but because one of them is squared, we write
Substituting, the equation finishes like
In other words, a quadratic equation:
We multiply the full equation by 9:
We solve it:
Therefore,
So, we obtain
The second option is not possible because it is negative. Therefore,
From where we obtain
More examples: 25 solved exponential equations
Matesfacil.com by J. Llopis is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.