# Exponential Equations Calculator

Enter the exponential equation and the variable for which to solve. Enter 2^x=10 and x to solve the equation for x. Use * to indicate multiplication of a number and a variable. Enter 2^(2*x)=10, instead of 2^(2x)=10.

**Solutions:**

**Examples:**

- To solve \(2^x+3x=10\), enter 2^x+3*
*x*=10 and the variable*x*. - To solve \((\frac{2}{3})^t=\frac{4}{3}\), enter (2/3)^t=4/3 and the variable
*t*. - To solve \(x^{2x}=20\), enter x^(2*x)=10 and the variable
*x*.

Use this calculator to find the solution to an exponential equation. Enter the equation and the solution will be displayed at the bottom.

## How to use the exponential equation calculator?

**Step 1:** The exponential equation must be entered in the first input box. The equation can contain any variable. Use the * sign to indicate multiplication between variables and coefficients. For example, 2x, should be written 2*x.

**Step 2:** Enter the variable to solve for in the second input box. For example, if the exponential equation is \( 3^x=20\), enter the variable *x*.

**Step 3:** Click “Solve” to get the solution to the exponential equation.

**Step 4:** The solution along with the entered equation will be displayed at the bottom.

## How to enter exponential expressions in the calculator?

You can use the ^ sign to indicate an exponent or an exponential expression. Also, you must use * to indicate multiplication between variables and coefficients. For example,

- To solve \(4^x-2=20\), enter 4^x-2=20 and the variable
*x*. - To solve \((\frac{1}{3})^t=\frac{4}{3}\), enter (1/3)^t=4/3 and the variable
*t*. - To solve \(a^{2a}=30\), enter a^(2*a)=30 and the variable
*a*.

Use parentheses to enter the expression correctly. For example, by writing a^(2*a), we indicate that the entire expression inside the parentheses is the exponent.

## What are exponential equations?

Exponential equations are equations where the variable appears as the exponent. For example, \( 3^x=81\) is an exponential equation. These equations have the general form \( b^x=c\). These equations are characterized by very rapid changes when changing the value of the variable.

If you want to learn more about equations and exponential functions, visit our article on exponential functions.

## What are the applications of exponential equations?

Exponential equations have diverse applications in various areas. One of the best-known applications is the modeling of exponential growth. This can be applied to model population growth or disease spread.

Furthermore, we can also use exponential equations to model the growth of bacterial populations.

Another well-known application is in finance with compound interest equations. The equations of accumulated interest over the years have an exponential form.

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