# Solving exponential equations with x as the exponent

• Tyrion101
In summary, the confusion is about basic exponent rules and whether both sides of an equation must have the same level of exponent when reducing the base for solving. The answer is that the exponents do not have to be the same, but the bases must be the same. This rule applies when the base is not 1 or 0.
Tyrion101
My confusion comes from basic exponent rules and whether or not both sides of an equation have to have the same level of exponent, when you reduce the base for solving. If one side can have an exponent of 3, does the other side also have to be reduced to something that would also have an exponent of 3? 9^2 does equal 81, but is that wrong if the other side can be reduced to a 3rd power, and can't be for a 2nd? I hope I'm making sense.

Tyrion101 said:
My confusion comes from basic exponent rules and whether or not both sides of an equation have to have the same level of exponent, when you reduce the base for solving. If one side can have an exponent of 3, does the other side also have to be reduced to something that would also have an exponent of 3? 9^2 does equal 81, but is that wrong if the other side can be reduced to a 3rd power, and can't be for a 2nd? I hope I'm making sense.
The exponents don't have to be the same, but the bases have to be the same if you're using this idea: am = an ##\Rightarrow## m = n.

1 person
Ok I think I understand

Just to nit pick, that is true when a =\= 1 and a =\= 0.

1 person

I can understand your confusion with solving exponential equations. Exponents can be tricky, but there are certain rules that can help us solve them correctly.

Firstly, it is important to remember that when solving an exponential equation, the goal is to isolate the variable (in this case, x) on one side of the equation. In order to do this, we need to use the properties of exponents to manipulate the equation.

One of the properties of exponents is the power rule, which states that when you have an exponent raised to another exponent, you can multiply the exponents together. For example, (x^2)^3 can be simplified to x^6.

In your example, 9^2 does equal 81, but this does not mean that the other side of the equation also has to have an exponent of 2. The key is to make sure that the exponents on both sides of the equation are equal after simplifying.

For instance, if one side of the equation has an exponent of 3, you can reduce the other side to a 3rd power as well. This could involve using the power rule or other exponent properties, such as the product rule or quotient rule.

In summary, the important thing to remember is that both sides of the equation do not have to have the same level of exponent, but they should have equal exponents after simplifying. I hope this helps to clarify your confusion.

## 1. What is an exponential equation?

An exponential equation is an equation in which the variable appears in the exponent. The general form of an exponential equation is y = abx, where a and b are constants and x is the variable.

## 2. How do I solve an exponential equation with x as the exponent?

To solve an exponential equation with x as the exponent, you can use logarithms. Take the logarithm of both sides of the equation and then use the power rule to bring the exponent down as a coefficient. From there, you can solve for x.

## 3. Can an exponential equation have more than one solution?

Yes, an exponential equation can have more than one solution. In fact, most exponential equations have an infinite number of solutions. This is because the variable is in the exponent and can take on a wide range of values.

## 4. Are there any special cases when solving exponential equations with x as the exponent?

Yes, there are two special cases when solving exponential equations with x as the exponent. The first is when the base is equal to 1, in which case the solution is any real number. The second is when the base is equal to 0, in which case there is no solution.

## 5. Can I use a calculator to solve exponential equations with x as the exponent?

Yes, you can use a calculator to solve exponential equations with x as the exponent. Most scientific calculators have a logarithm function that can help you solve these types of equations. However, it is important to understand the steps and principles behind solving exponential equations before relying on a calculator.

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