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Trigonometry Examples
Step 1
Step 1.1
Rewrite the equation as .
Step 1.2
Move all the terms containing a logarithm to the left side of the equation.
Step 1.3
Simplify the left side.
Step 1.3.1
Simplify .
Step 1.3.1.1
Simplify by moving inside the logarithm.
Step 1.3.1.2
Use the quotient property of logarithms, .
Step 1.3.1.3
Use the quotient property of logarithms, .
Step 1.3.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 1.3.1.5
Combine.
Step 1.3.1.6
Multiply by .
Step 1.4
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 1.5
Solve for .
Step 1.5.1
Rewrite the equation as .
Step 1.5.2
Multiply both sides by .
Step 1.5.3
Simplify.
Step 1.5.3.1
Simplify the left side.
Step 1.5.3.1.1
Simplify .
Step 1.5.3.1.1.1
Rewrite using the commutative property of multiplication.
Step 1.5.3.1.1.2
Cancel the common factor of .
Step 1.5.3.1.1.2.1
Factor out of .
Step 1.5.3.1.1.2.2
Cancel the common factor.
Step 1.5.3.1.1.2.3
Rewrite the expression.
Step 1.5.3.1.1.3
Cancel the common factor of .
Step 1.5.3.1.1.3.1
Cancel the common factor.
Step 1.5.3.1.1.3.2
Rewrite the expression.
Step 1.5.3.2
Simplify the right side.
Step 1.5.3.2.1
Simplify .
Step 1.5.3.2.1.1
Anything raised to is .
Step 1.5.3.2.1.2
Multiply by .
Step 1.5.4
Solve for .
Step 1.5.4.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.5.4.2
The complete solution is the result of both the positive and negative portions of the solution.
Step 1.5.4.2.1
First, use the positive value of the to find the first solution.
Step 1.5.4.2.2
Next, use the negative value of the to find the second solution.
Step 1.5.4.2.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2
Step 2.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2.2
Divide each term in by and simplify.
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of .
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Divide by .
Step 2.3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Interval Notation:
Set-Builder Notation:
Step 3
The expression is continuous.
Continuous
Step 4