Precalculus : Pre-Calculus

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #2 : Exponential Equations And Inequalities

Solving an exponential equation.

Solve

Possible Answers:

Correct answer:

Explanation:

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

.

Example Question #3 : 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 #4 : 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 #2 : 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 .

Example Question #1231 : Pre Calculus

Solve for x: 

Possible Answers:

Correct answer:

Explanation:

Example Question #1232 : Pre Calculus

Solve for x in the following equation: 

Possible Answers:

Correct answer:

Explanation:

Example Question #1233 : Pre Calculus

Solve for x using the rules of logarithms: 

Possible Answers:

Correct answer:

Explanation:

Example Question #4 : Use Logarithms To Solve Exponential Equations And Inequalities

Solve for x: 

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Use Logarithms To Solve Exponential Equations And Inequalities

Simplify the log expression: 

Possible Answers:

Cannot be simplified any further

Correct answer:

Cannot be simplified any further

Explanation:

The logarithmic expression is as simplified as can be. 

 

Example Question #1 : Solve A System Of Quadratic Equations

Which of the following could NOT be a possible number of solutions of a system of quadratic and linear equations? 

Possible Answers:

3

How many times the graphs intersect 

0

1

Correct answer:

3

Explanation:

Recall that the solution of a system of equations is given by the intersection points of the graphs. Thus, this question is really asking how many times a parabola and a line can intersect. Visualize a parabola and a line. For this purpose, let's say that the parabola is facing up. If a line is drawn horizontally under the vertex, then it would not intersect the parabola at all, so the system would have no solutions. If the line is tangent to, or just skims the edge, of the parabola then it would only intersect once and the system would have one solution. If the line goes straight through the parabola, then it would intersect twice. There is no other option for the orientation of the line and parabola. Thus, there cannot be three solutions. 

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