When solving exponential equations, we need to ensure that we have the same base. When that happens, our equations our based on the exponents. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply the power rule of 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. However, since the base is different, we can definitely convert one of the numbers to have the same base. We know that 

 therefore

 Apply the power rule of exponents.

 With the same base, we can now write

 Add  on both sides.

Solve by first changing the base of the right side.

Rewrite the equation.

With common bases, we can set the powers equal to each other.

Use distribution to simplify the right side.

Add  on both sides.

Add two on both sides.

Divide by 9 on both sides.

The answer is:  

In order to solve this equation, we will need to change the base of one half to two. Use a negative exponent to rewrite this term.

Rewrite the equation.

Since the bases are common, we can simply set the exponents equal to each other.

Solve for x.  Divide a negative one on both sides to eliminate the negatives.

The equation becomes:

Subtract  from both sides.

Divide both sides by negative four.

The answer is:  

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 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 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 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.

 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. Since the bases are now different, we need to convert so we have the same base. We do know that

 therefore

 With the same base, we can now 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. Since the bases are now different, we need to convert so we have the same base. We do know that

 therefore

 With the same base, we can now write

 Add  on both sides.

 Divide  on both sides.