Solving Exponential Equations

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

With same base, we can write:

Subtract on both sides.

Divide on both sides.

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

With the same base, we can now write

Subtract on both sides.

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

With the same base, we can now write

Add and subtract on both sides.

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

With the same base, we can write:

Add on both sides.

Divide on both sides.

When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents.

With the same base, we can now write

Take the square root on both sides. Account for negative answer.

When dealing with exponential equations, we want to make sure the bases are the same. This way we can set-up an equation with the exponents.

With the same base, we can now write

Subtract on both sides.

Because both sides of the equation have the same base, set the terms equal to each other.

Add 9 to both sides:

Then, subtract 2x from both sides:

Finally, divide both sides by 3:

When we add exponents, we try to factor to see if we can simplify it. Let's factor . We get . Remember to apply the rule of multiplying exponents which is to add the exponents and keeping the base the same.

With the same base, we can rewrite as .

Rewrite the right side of the equation using a base of ten.

One thousand to the power of x can be rewritten using the product of exponents.

Now that the bases are equal, set the powers equal to each other.

Subtract from both sides.

Simplify both sides.

The answer is: