# Exponential equation

An equation is exponential if the variable (unknown) appears in the exponent of a power. To solve this type of equations we have to remember all the potentiation properties. In some cases variable changes are made to make your solution easier. The general expression of a exponential equation is the next: Where, a and b are real numbers, x is the exponent of the expression and the unknown of the equation. Knowing that the general expression of an exponential equation is ax - b = 0We will look for a way to find the value of the unknown variable through the application of clearances and power properties.

## How to solve an exponential equation?

To understand how to solve such an equation, we must perform some exercises:

### Exponential Equation Exercises

Exercise 1: Find the value of x in the following equation 2x + 1 = 8.

We will first transform 8 into base 2 power: We rewrite the equation: Since the bases are equal, the exponents are equalized and we solve for x:   Now, let's check that this value of x is a solution to the equation:   So x = 2 is the solution to our exponential equation.

Exercise 2: Find the value of x in the following equation 35x + 2 = 6561.

We transform 6561 into base 3 power: We rewrite the equation: Since the bases are equal, the exponents are equalized and we solve for x:   To verify that x = 6/5 is a solution, we substitute it in the equation:   So x = 6/5 is the solution to our exponential equation.

Exercise 3: Find the value of x in the following equation 5x2 + 5x = 1/625.

We will first express 625 in base 5 power: We rewrite the equation Applying the property to-n = 1 / an, we have: Since the bases are equal, the exponents are equalized: Remaining an equation of second degree: Using the quadratic formula: We will have the values of x solution to the exponential equation:  Exercise 4: Find the value of x in the following equation: Applying the power property ton·tom = ton + m  we have: We take common factor 2x : To terms 2- two and 2- 3  we apply the power property to-n = 1 / an:       At MiProfe we offer you school support in Mathematics, Physics, Chemistry, Electronics, Languages (English, French, German and Portuguese) and Accounting. Hire your online class no matter where you are. We have a private online teacher for you who can help you on the day and time that best suits you, even on weekends! So choose the plan that goes better with you and start learning with us now: