Exponential Equation Example

” Equations” is a very important subject in Algebra, mastering it requires practice and being consistent with your study.

Thinking about it, we bring you an exponential equation exercise that was published on the mind plus channel and that, in our opinion, is a nice example of how to solve a mathematical problem.

The exercise is as follows;

You are asked to calculate the value of “x” in the equation:

5^3x-4 = 1

At first glance it is an exercise that scares anyone, because the variable or unknown is as an exponent of the number 5; however, the author starts the solution by stating that he will apply the following property:

And:

a^m = aⁿ

Furthermore: a>0, it is fulfilled:

m = n

That is, the property indicates if the bases are equal, and if it is greater than zero, then it is true that the exponents must be equal.

He also performs a trick with the expression on the left side of the equation, that is, with “1”, observe:

1 = 5⁰

So in the initial equation:

5^3x-4 = 5⁰

The exponents are equalized according to the property seen.

⇒ 3x – 4 = 0

Developing this linear equation, we have:

x = 3/4

As you can see, it is a nice exercise that deserves our attention, for more detail you can see the following video that was published.