GRE Subject Test: Math : Exponential Functions

Example Questions

Example Question #11 : Exponential Functions

Solve this exponential equation for

Explanation:

Isolate the variable by dividing by 6.

is the same as .

Example Question #12 : Exponential Functions

Explanation:

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

Explanation:

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

Explanation:

To solve, use the natural .

Example Question #14 : Exponential Functions

Explanation:

Divide both sides by

Write in logarithm form and solve for

Divide both sides by

Example Question #15 : Exponential Functions

Explanation:

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:

Explanation:

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

Explanation:

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:

Explanation:

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

Explanation:

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,