# Evaluate log base 5 of 5x-2> log base 5 of 2x+10

Convert the inequality to an equality.
Solve the equation.
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Solve for .
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Find the domain of .
Set the argument in greater than to find where the expression is defined.
Solve for .
Find all the values where the expression switches from negative to positive by setting each factor equal to and solving.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Subtract from both sides of the equation.
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
Consolidate the solutions.
Find the domain of .
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Subtract from both sides of the equation.
The domain is all values of that make the expression defined.
Interval Notation:
Interval Notation:
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not greater than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
or
or
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Subtract from both sides of the equation.
The domain is all values of that make the expression defined.
Interval Notation:
Interval Notation:
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not equal to the right side, which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
Determine if the inequality is true.
Rewrite the equation in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
The left side does not equal to the right side , which means that the given statement is false.
False
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
Determine if the inequality is true.
Rewrite the equation in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
The left side does not equal to the right side , which means that the given statement is false.
False
False
False
Compare the intervals to determine which ones satisfy the original inequality.
False
False
False
False
False
False
Since there are no numbers that fall within the interval, this inequality has no solution.
No solution
Convert the inequality to an equality.
Solve the equation.
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Solve for .
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Find the domain of .
Set the argument in greater than to find where the expression is defined.
Solve for .
Find all the values where the expression switches from negative to positive by setting each factor equal to and solving.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Subtract from both sides of the equation.
Solve for each factor to find the values where the absolute value expression goes from negative to positive.
Consolidate the solutions.
Find the domain of .
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Subtract from both sides of the equation.
The domain is all values of that make the expression defined.
Interval Notation:
Interval Notation:
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not greater than the right side , which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is greater than the right side , which means that the given statement is always true.
True
True
Compare the intervals to determine which ones satisfy the original inequality.
True
False
True
True
False
True
The solution consists of all of the true intervals.
or
or
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Subtract from both sides of the equation.
The domain is all values of that make the expression defined.
Interval Notation:
Interval Notation:
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not equal to the right side, which means that the given statement is false.
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
Determine if the inequality is true.
Rewrite the equation in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
The left side does not equal to the right side , which means that the given statement is false.
False
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
Determine if the inequality is true.
Rewrite the equation in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
The left side does not equal to the right side , which means that the given statement is false.
False
False
False
Compare the intervals to determine which ones satisfy the original inequality.
False
False
False
False
False
False
Since there are no numbers that fall within the interval, this inequality has no solution.
No solution
Evaluate log base 5 of 5x-2> log base 5 of 2x+10