Question

How to solve exponential equation?​

Answer 1

Explanation:

To solve an exponential equation, you need to first identify what the base and the exponent are. The base is the number being multiplied by itself and the exponent is the number of times it is being multiplied.

Next, you will need to use the property of exponents that states that if the bases are the same, you can set the exponents equal to each other. For example, if you have the equation 3^x = 9, you can set the exponents equal to each other and solve for x by dividing both sides by 3. This gives you x = 2.

If you have an equation with different bases, you will need to use logarithms to solve it. Logarithms are the inverse of exponents, meaning that if you take the logarithm of an exponential equation, it will turn it into a linear equation that you can solve using algebra.

For example, if you have the equation 2^x = 8, you can take the logarithm of both sides to get x = (2^x) = (8). Since (2) = 0.301, and (8) = 0.903, you can solve for x by dividing both sides by (2) to get x = 3.

Overall, solving exponential equations requires a combination of understanding the properties of exponents and using logarithms to turn the equation into a form that you can solve using algebra.

Answer 2

To solve an exponential equation, you need to find the values of the variables that make the equation true. Here are some steps you can follow:

Identify the base of the exponential function. This will usually be denoted by a letter such as "b" or "a".

Move all the terms that do not contain the exponential function to one side of the equation.

Isolate the exponential function on the other side of the equation.

Use the properties of exponential functions to simplify the equation. For example, you can use the fact that b^x * b^y = b^(x+y) when b is the same in both exponents.

Solve the equation by finding the values of the variables that make the equation true.

For example, consider the equation 3^x = 9. To solve this equation:

The base of the exponential function is 3.

Move the 9 to the right side of the equation: 3^x - 9 = 0

Isolate the exponential function on the left side: 3^x = 9

Use the property of exponential functions to simplify: 3^2 = 9

Solve for x: x = 2

The solution to the equation is x = 2.