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Trigonometry Examples
Step 1
Step 1.1
Use the product property of logarithms, .
Step 1.2
Expand using the FOIL Method.
Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify and combine like terms.
Step 1.3.1
Simplify each term.
Step 1.3.1.1
Rewrite using the commutative property of multiplication.
Step 1.3.1.2
Multiply by by adding the exponents.
Step 1.3.1.2.1
Move .
Step 1.3.1.2.2
Multiply by .
Step 1.3.1.3
Multiply by .
Step 1.3.1.4
Multiply by .
Step 1.3.1.5
Multiply by .
Step 1.3.1.6
Multiply by .
Step 1.3.2
Subtract from .
Step 2
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 3
Step 3.1
Rewrite the equation as .
Step 3.2
Raise to the power of .
Step 3.3
Move all terms to the left side of the equation and simplify.
Step 3.3.1
Subtract from both sides of the equation.
Step 3.3.2
Subtract from .
Step 3.4
Use the quadratic formula to find the solutions.
Step 3.5
Substitute the values , , and into the quadratic formula and solve for .
Step 3.6
Simplify.
Step 3.6.1
Simplify the numerator.
Step 3.6.1.1
Raise to the power of .
Step 3.6.1.2
Multiply .
Step 3.6.1.2.1
Multiply by .
Step 3.6.1.2.2
Multiply by .
Step 3.6.1.3
Add and .
Step 3.6.1.4
Rewrite as .
Step 3.6.1.4.1
Factor out of .
Step 3.6.1.4.2
Rewrite as .
Step 3.6.1.5
Pull terms out from under the radical.
Step 3.6.2
Multiply by .
Step 3.6.3
Simplify .
Step 3.7
The final answer is the combination of both solutions.
Step 4
Exclude the solutions that do not make true.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: