Trigonometry Examples

Solve for x ( log of 16-x^2)/( log of 3x-4)=2
Step 1
Find the LCD of the terms in the equation.
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Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
The LCM of one and any expression is the expression.
Step 2
Multiply each term in by to eliminate the fractions.
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Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Rewrite the expression.
Step 2.3
Simplify the right side.
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Step 2.3.1
Simplify by moving inside the logarithm.
Step 3
Solve the equation.
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Step 3.1
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Step 3.2
Solve for .
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Rewrite.
Step 3.2.1.2
Rewrite as .
Step 3.2.1.3
Expand using the FOIL Method.
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Step 3.2.1.3.1
Apply the distributive property.
Step 3.2.1.3.2
Apply the distributive property.
Step 3.2.1.3.3
Apply the distributive property.
Step 3.2.1.4
Simplify and combine like terms.
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Step 3.2.1.4.1
Simplify each term.
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Step 3.2.1.4.1.1
Rewrite using the commutative property of multiplication.
Step 3.2.1.4.1.2
Multiply by by adding the exponents.
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Step 3.2.1.4.1.2.1
Move .
Step 3.2.1.4.1.2.2
Multiply by .
Step 3.2.1.4.1.3
Multiply by .
Step 3.2.1.4.1.4
Multiply by .
Step 3.2.1.4.1.5
Multiply by .
Step 3.2.1.4.1.6
Multiply by .
Step 3.2.1.4.2
Subtract from .
Step 3.2.2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 3.2.3
Move all terms containing to the left side of the equation.
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Step 3.2.3.1
Add to both sides of the equation.
Step 3.2.3.2
Add and .
Step 3.2.4
Subtract from both sides of the equation.
Step 3.2.5
Combine the opposite terms in .
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Step 3.2.5.1
Subtract from .
Step 3.2.5.2
Add and .
Step 3.2.6
Factor out of .
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Step 3.2.6.1
Factor out of .
Step 3.2.6.2
Factor out of .
Step 3.2.6.3
Factor out of .
Step 3.2.7
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.2.8
Set equal to .
Step 3.2.9
Set equal to and solve for .
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Step 3.2.9.1
Set equal to .
Step 3.2.9.2
Solve for .
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Step 3.2.9.2.1
Add to both sides of the equation.
Step 3.2.9.2.2
Divide each term in by and simplify.
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Step 3.2.9.2.2.1
Divide each term in by .
Step 3.2.9.2.2.2
Simplify the left side.
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Step 3.2.9.2.2.2.1
Cancel the common factor of .
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Step 3.2.9.2.2.2.1.1
Cancel the common factor.
Step 3.2.9.2.2.2.1.2
Divide by .
Step 3.2.10
The final solution is all the values that make true.
Step 4
Exclude the solutions that do not make true.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: