Precalculus : Use Logarithms To Solve Exponential Equations and Inequalities

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Use Logarithms To Solve Exponential Equations And Inequalities

Solving an exponential equation.

Solve for ,

.

Possible Answers:

Correct answer:

Explanation:

We recall the property:

Now, .

Thus

.

Example Question #1 : Use Logarithms To Solve Exponential Equations And Inequalities

Solving an exponential equation.

Solve

Possible Answers:

Correct answer:

Explanation:

Use  (which is just , by convention) to solve.

.

Example Question #1 : Use Logarithms To Solve Exponential Equations And Inequalities

Solve the equation for  using the rules of logarithms.

Possible Answers:

Correct answer:

Explanation:

Expanding the logarithms into sums of logarithms will cancel out the first two x terms, resulting in the equation:

 

Combining the first and second terms, then subtracting the new term over will allow you to isolate the variable term.

Divide both sides of the equation by 2, then exponentiate with 3.

Evaluating this term numerically will give the correct answer.

Example Question #2 : Use Logarithms To Solve Exponential Equations And Inequalities

Solve the following equation:

Possible Answers:

Correct answer:

Explanation:

To solve this equation, recall the following property:

     Can be rewritten as 

Evaluate with your calculator to get

Example Question #3 : Use Logarithms To Solve Exponential Equations And Inequalities

Solve 

.

Possible Answers:

Correct answer:

Explanation:

After using the division rule to simplify the left hand side you can take the natural log of both sides.

If you then combine like terms you get a quadratic equation which factors to,

 .

Setting each binomial equal to zero and solving for  we get the solution to be .

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