Solve exponential equation?

To solve an exponential equation, you can follow these steps:

1. If the bases of the exponential terms are the same, you can set the exponents equal to each other and solve for the variable. For example, if you have the equation 2^x = 8^2, you can rewrite 8 as 2^3 and then set the exponents equal to each other: x = 3*2 = 6.

2. If the bases are not the same, you can rewrite the terms with the same base and then set the exponents equal to each other. For example, if you have the equation 3^x = 9^2, you can rewrite 9 as 3^2 and then set the exponents equal to each other: x = 2*2 = 4.

3. If the equation is more complex, you may need to use logarithms to solve for the variable. For example, if you have the equation 5^x = 125, you can take the logarithm of both sides to solve for x: x = log(125)/log(5) = 3.

Remember to always check your solution by plugging it back into the original equation to ensure it is correct.

Steps to Solve Exponential Equations:

1. Isolate the Exponential Term:
Move all terms with the exponential variable to one side of the equation.

2. Rewrite as a Logarithmic Equation:
Take the logarithm of both sides of the equation using the appropriate base.
```
log(base)(exponential term) = logarithm of the other side
```

3. Simplify the Logarithm:
Use the properties of logarithms to simplify the expression.

4. Solve for the Variable:
Solve the logarithmic equation for the variable using algebra.

5. Check the Solution:
Plug the solution back into the original equation to ensure it satisfies the equality.

Example:

Solve the exponential equation: 2^x = 16

Solution:

1. Isolate the Exponential Term:
```
2^x = 16
```

2. Rewrite as a Logarithmic Equation:
```
log2(2^x) = log2(16)
```

3. Simplify the Logarithm:
```
x log2(2) = log2(16)
```
```
x = log2(16)
```

4. Solve for x:
```
x = 4
```

5. Check the Solution:
Plugging x = 4 into the original equation gives:
```
2^4 = 16
```
```
16 = 16
```
The solution is correct.