GRE Subject Test: Math : Solving Exponential Equations

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

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Example Question #1 : Solving Exponential Equations

Find one possible value of , given the following equation:

Possible Answers:

Cannot be determined from the information given.

Correct answer:

Explanation:

We begin with the following:

This can be rewritten as

Recall that if you have two exponents with equal bases, you can simply set the exponents equal to eachother. Do so to get the following:

Solve this to get t.

Example Question #2 : Solving Exponential Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

We need to make the bases equal before attempting to solve for . Since  we can rewrite our equation as

    Remember: the exponent rule 

Now that our bases are equal, we can set the exponents equal to each other and solve for 

 

Example Question #323 : Gre Subject Test: Math

Solve for 

Possible Answers:

Correct answer:

Explanation:

The first step is to make sure we don't have a zero on one side which we can easily take care of: 

Now we can take the logarithm of both sides using natural log:

Note: we can apply the Power Rule here 

Example Question #3 : Solving Exponential Equations

Solve for 

Possible Answers:

Correct answer:

Explanation:

Before beginning to solve for , we need  to have a coefficient of 

Now we can take the natural log of both sides:

Note: 

Example Question #325 : Gre Subject Test: Math

Possible Answers:

Correct answer:

Explanation:

Since the base is  for both, then:


  When the base is the same, and you are multiplying, the exponents are added.

 

Example Question #1 : Exponential Functions

Possible Answers:

Correct answer:

Explanation:

To solve, use common 

Example Question #5 : Solving Exponential Equations

Possible Answers:

Correct answer:

Explanation:

To solve, use the natural log.

To isolate the variable, divide both sides by .

Example Question #6 : Solving Exponential Equations

Possible Answers:

Correct answer:

Explanation:

To solve, use the natural log.

Example Question #7 : Solving Exponential Equations

Solve the equation.  Express the solution as a logarithm in base-10.

Possible Answers:

Correct answer:

Explanation:

Isolate the exponential part of the equation.

Convert to log form and solve.

 can also be written as .

 

Example Question #8 : Solving Exponential Equations

Possible Answers:

Correct answer:

Explanation:

Simply the exponential part of the equation by dividing both sides by

Write in logarithm form.

Because  is also written as 

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