### All GRE Subject Test: Math Resources

## Example Questions

### Example Question #11 : Exponential Functions

Solve this exponential equation for

**Possible Answers:**

**Correct answer:**

Isolate the variable by dividing by 6.

is the same as .

### Example Question #12 : Exponential Functions

**Possible Answers:**

**Correct answer:**

Isolate by adding to both sides of the exponential equation.

Take the common log.

Use logarithmic rule 3. An exponent inside a log can be moved outside as a multiplier.

Simplify. Because

Isolate the variable by subtracting from both sides.

### Example Question #11 : Exponential Functions

**Possible Answers:**

**Correct answer:**

Simplify by dividing both sides by

Subtract from both sides of the exponential equation.

Since base is 7, take log 7 of both sides.

Use logarithmic rule 3. An exponent on everything inside a log can be moved out front as a multiplier,

Simplify by dividing both sides of the exponential equation by 2.

### Example Question #13 : Exponential Functions

**Possible Answers:**

**Correct answer:**

To solve, use the natural .

### Example Question #14 : Exponential Functions

**Possible Answers:**

**Correct answer:**

Divide both sides by

Write in logarithm form and solve for

Divide both sides by

### Example Question #15 : Exponential Functions

**Possible Answers:**

**Correct answer:**

Isolate the variable by dividing both sides of the equation by

Write in logarithm form.

Because the solution is in base-3 log, it can be changed to base -10 by using:

### Example Question #16 : Exponential Functions

Solve for x:

**Possible Answers:**

**Correct answer:**

Step 1: Rewrite the right side of the equation into a power of 2.

Step 2: We have the same base, so we can equate the exponents.

Step 3: Solve for x. We will subtract 1 from both sides to isolate x.

### Example Question #17 : Exponential Functions

Solve for :

**Possible Answers:**

**Correct answer:**

Step 1: Rewrite as .

Step 2: Re-write the equation:

Step 3: By laws of exponents, if the bases are the same, we can equate the exponents...

We will get

Step 4: Move 10 over and begin factoring:

Step 5: is a correct answer... we can plug it in and see:

Step 6: is the other correct answer...

### Example Question #19 : Exponential Functions

Solve:

**Possible Answers:**

**Correct answer:**

Step 1: Rewrite the right hand side of the equation as a power of 2.

. To get this, divide the base by 2 and multiply that 2 to the exponent...

Step 2: Equate the left and right side together

We have the same base, so we equate the exponents together..

...

### Example Question #18 : Exponential Functions

Solve for :

**Possible Answers:**

**Correct answer:**

Step 1: Write as ...

Step 2: Rewrite as in the original equation..

Step 3: By a rule of exponents, I can set the exponents equal if the bases of both exponents are the same...

So,