# Algebra II : Solving Exponential Equations

## Example Questions

### Example Question #91 : Solving Exponential Equations

Solve the equation:

Explanation:

We can rewrite the left side of the equation as follows:

Rewrite the equation.

Since both sides share the same bases, we can set the powers equal to each other.

Solve for x.

Subtract  on both sides.

Divide by three on both sides.

### Example Question #92 : Solving Exponential Equations

Solve:

Explanation:

Rewrite the right side using three as the base.

The equation becomes:

Since both sides share similar bases, we can set the powers equal to each other.

Divide both sides by 37.

### Example Question #93 : Solving Exponential Equations

Solve:

Explanation:

We can rewrite the right side by changing the base.

Rewrite the right side using the new base.

Now that the bases are similar, we can set the exponents equal to each other.

Subtract  on both sides.

Divide by four on both sides.

Reduce the fractions.

### Example Question #94 : Solving Exponential Equations

Solve the equation:

Explanation:

We will need to convert the bases on both sides to base three.

Rewrite the equation.

Simplify both sides.

On the left side, notice that a lone three is the coefficient of the base.  We will need to write the left side such that:

Recall that if the powers of the same base are multiplied, the powers can be added.

Simplify the exponent.

The equation becomes:

Set the exponential terms equal to each other now that the bases are equal.

Divide by negative three on both sides.

### Example Question #95 : Solving Exponential Equations

Solve:

Explanation:

Change the base of the second term to base two.

Simplify the right side by multiplying the exponents.

Now that the bases are common, the exponents can be set equal to each other.

Subtract  from both sides.

Divide by negative 18 on both sides.

### Example Question #96 : Solving Exponential Equations

Solve:

Explanation:

To evaluate this equation, we will need to change the base of the left side.

Rewrite the equation.

Now that both bases are similar, we can set the exponents equal to each other.

Divide by three on both sides.

### Example Question #97 : Solving Exponential Equations

Solve the equation:

Explanation:

Rewrite both sides of the equation so that we have same bases.

Simplify the exponents.

Add the exponents on the left side.

Now that both sides have same bases, we can set the exponential terms equal.

### Example Question #98 : Solving Exponential Equations

Solve:

Explanation:

In order to solve this, we will need to rewrite the fractional base to base three.

Rewrite the equation using this base.

Now that both bases are common, we can set up an equation where the powers are equal.

Use distribution to simplify the right side.

Subtract nine from both sides.

Divide by negative 27 on both sides.

### Example Question #99 : Solving Exponential Equations

Evaluate:

Explanation:

To solve this exponential equation, we will need to change the base of the second term.  Notice that both the numerator and denominator are the values of the left fraction cubed.

Rewrite the equation.

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

Distribute the right side.

Divide by six on both sides.

### Example Question #100 : Solving Exponential Equations

Solve:

Explanation:

In order to solve this equation, we will need to change the base of the left side.

Rewrite one-ninth as base three.

Rewrite the equation.

Now that both bases are common, we can set both powers equal.

Simplify the left side and solve for x.

Add 10 on both sides, and then divide by two.