All High School Math Resources
Example Questions
Example Question #171 : Algebra Ii
Solve for :
The equation has no solution.
Since , , and we can rewrite and solve this statement as follows:
Substitution confirms this to be the only solution.
Example Question #22 : Logarithms
Solve for :
The equation has no solution.
The solution set of the equation is the set of all real numbers.
We can rewrite this as follows:
Split this into a compound statement, and solve:
Test both of these possible solutions by substituting:
Since only positive numbers can have logarithms, this equation does not make sense. is not a solution.
is a solution - the only solution.
Example Question #173 : Algebra Ii
What is the sum of the value(s) of x that satisfy the equation ?
20
35
No solution.
100
35/2
35/2
We need to rewrite the logarithmic equation into a form that is more recognizable.
An equation in the form can be rewritten in the exponential form , where a, b, and c are constants (and b > 0). Thus, we will rewrite our original equation as follows:
.
We can now approach this as we would a typical quadratic equation.
Subtract 100 from both sides. We need to set all of the terms equal to zero.
.
We can factor this by first multiplying the outer coefficients. The product of 2 and -100 is equal to -200. We must think of two numbers that multiply to give -200 but add to give -35 (the middle coefficient). Two numbers that satisfy both of these requirements are -40 and 5. We will now rewrite the quadratic polynomial.
We can use grouping to factor the polynomial. Factor the first two terms and the last two terms separately.
Notice that we can now factor out x - 20 from the 2x term and the 5 term.
To solve this, we set each factor equal to zero.
The question ultimately asks for the sum of the values of x that satisfy the equation, so we must add -5/2 and 20, which yields 35/2.
The answer is 35/2.
Example Question #15 : Solving Logarithmic Equations
Solve the following logarithmic equation:
Since the bases of the logs are the same and the logarithms are added, the arguments can be multiplied together.
The logarithm can then be converted to exponential form.
Although there are two solutions to the equation, logarithims cannot be negative. Therefore, the only real solution is .
Example Question #25 : Logarithms
Solve the following logarithmic equation:
Start by converting the logarithms into exponential form:
Convert again into exponential form:
Simplify and solve:
Example Question #23 : Logarithms
Solve the following logarithmic equation:
Since the bases of the logs are the same, the terms inside the logs can be set equal to each other.
Example Question #13 : Solving Logarithmic Equations
Solve the equation.
Change the right side to so that both sides are the same. Apply log to both sides so that you can set the exponential expressions equal to each other ().
Example Question #171 : Mathematical Relationships And Basic Graphs
What is the value of ?
6
10
24
4
12
24
! is the symbol for factorial, which means the product of the whole numbers less than the given number.
Thus, .
Example Question #1 : Factorials
What is the value of ?
By definition, .
Example Question #3 : Factorials
Find the value of:
The factorial sign (!) just tells us to multiply that number by every integer that leads up to it. So, can also be written as:
To make this easier for ourselves, we can cancel out the numbers that appear on both the top and bottom: