All Precalculus Resources
Example Questions
Example Question #2 : Exponential Equations And Inequalities
Solving an exponential equation.
Solve
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.
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:
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
.
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:
Example Question #1232 : Pre Calculus
Solve for x in the following equation:
Example Question #1233 : Pre Calculus
Solve for x using the rules of logarithms:
Example Question #4 : Use Logarithms To Solve Exponential Equations And Inequalities
Solve for x:
Example Question #5 : Use Logarithms To Solve Exponential Equations And Inequalities
Simplify the log expression:
Cannot be simplified any further
Cannot be simplified any further
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?
3
How many times the graphs intersect
0
2
1
3
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.