# Algebra II : Solving Exponential Equations

## Example Questions

### Example Question #81 : Solving Exponential Equations

Solve for .

Explanation:

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

Divide  on both sides.

### Example Question #82 : Solving Exponential Equations

Solve for .

Explanation:

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.

### Example Question #83 : Solving Exponential Equations

Solve for .

Explanation:

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

Apply power rule of exponents.

With the same base, we can now write

Subtract  on both sides.

Divide  on both sides.

### Example Question #84 : Solving Exponential Equations

Solve for .

Explanation:

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

Apply power rule of exponents.

With the same base, we can now write

Subtract  on both sides.

### Example Question #85 : Solving Exponential Equations

Solve for .

Explanation:

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 and also applying power rule of exponents, we now can write

Divide  on both sides.

### Example Question #86 : Solving Exponential Equations

Solve for .

Explanation:

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 and by also applying the power rule of exponents, we can now write

Subtract  on both sides.

### Example Question #87 : Solving Exponential Equations

Solve:

Explanation:

In order to solve this equation, we will need to change the bases so that both bases are equal.  We can change the bases to base three.

Rewrite the terms in the equation.

The powers can be set equal to each other now that we have similar bases.

Solve for x.

Subtract  on both sides.

Divide by negative 12 on both sides.

### Example Question #88 : Solving Exponential Equations

Evaluate:

Explanation:

Evaluate by changing the base of the fraction.

Rewrite the equation.

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

Solve for x.

Subtract x from both sides.

Divide by negative ten on both sides.

### Example Question #89 : Solving Exponential Equations

Solve the equation:

Explanation:

Convert the right side to a base of 7.

With similar bases, the powers can be set equal to each other.

Multiply both sides by .

Subtract two from both sides.

Factorize the left term to determine the roots of the quadratic.

Set each binomial equal to zero and solve for x.

Ensure that both solutions will satisfy the original equation.  Since there is no zero denominator resulting from substitution, both answers will satisfy.

### Example Question #90 : Solving Exponential Equations

Solve:

Explanation:

Convert the right fraction to a base of two thirds.

Rewrite the right side.

With similar bases, set both powers equal to each other.

Simplify the right side by distribution.

Subtract  from both sides.

Divide both sides by negative seven.