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Trigonometry Examples
Step 1
Rewrite the equation as .
Step 2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 3
Step 3.1
Use to rewrite as .
Step 3.2
Expand by moving outside the logarithm.
Step 3.3
Multiply the numerator and denominator of by the conjugate of to make the denominator real.
Step 3.4
Multiply.
Step 3.4.1
Combine.
Step 3.4.2
Simplify the numerator.
Step 3.4.2.1
Apply the distributive property.
Step 3.4.2.2
Multiply by .
Step 3.4.2.3
Reorder factors in .
Step 3.4.3
Simplify the denominator.
Step 3.4.3.1
Expand using the FOIL Method.
Step 3.4.3.1.1
Apply the distributive property.
Step 3.4.3.1.2
Apply the distributive property.
Step 3.4.3.1.3
Apply the distributive property.
Step 3.4.3.2
Simplify.
Step 3.4.3.2.1
Multiply by .
Step 3.4.3.2.2
Multiply by .
Step 3.4.3.2.3
Raise to the power of .
Step 3.4.3.2.4
Raise to the power of .
Step 3.4.3.2.5
Use the power rule to combine exponents.
Step 3.4.3.2.6
Add and .
Step 3.4.3.2.7
Subtract from .
Step 3.4.3.2.8
Add and .
Step 3.4.3.3
Simplify each term.
Step 3.4.3.3.1
Rewrite as .
Step 3.4.3.3.2
Multiply by .
Step 3.4.3.4
Add and .
Step 3.5
Rewrite as .
Step 4
Step 4.1
Rewrite as .
Step 4.2
Use to rewrite as .
Step 4.3
Use to rewrite as .
Step 5
Step 5.1
Use the quotient property of logarithms, .
Step 6
Step 6.1
Simplify .
Step 6.1.1
Use the quotient property of logarithms, .
Step 6.1.2
Reorder factors in .
Step 7
Step 7.1
Divide each term in by .
Step 7.2
Simplify the left side.
Step 7.2.1
Cancel the common factor of .
Step 7.2.1.1
Cancel the common factor.
Step 7.2.1.2
Divide by .