Trigonometry Examples

Solve for x log base 12 of 2x+1=1-2 log base 12 of 2
Step 1
Move all the terms containing a logarithm to the left side of the equation.
Step 2
Simplify the left side.
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Step 2.1
Simplify .
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Step 2.1.1
Simplify each term.
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Step 2.1.1.1
Simplify by moving inside the logarithm.
Step 2.1.1.2
Raise to the power of .
Step 2.1.2
Use the product property of logarithms, .
Step 2.1.3
Apply the distributive property.
Step 2.1.4
Multiply.
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Step 2.1.4.1
Multiply by .
Step 2.1.4.2
Multiply by .
Step 3
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 4
Solve for .
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Step 4.1
Rewrite the equation as .
Step 4.2
Move all terms not containing to the right side of the equation.
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Subtract from .
Step 4.3
Divide each term in by and simplify.
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Step 4.3.1
Divide each term in by .
Step 4.3.2
Simplify the left side.
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Step 4.3.2.1
Cancel the common factor of .
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Step 4.3.2.1.1
Cancel the common factor.
Step 4.3.2.1.2
Divide by .
Step 4.3.3
Simplify the right side.
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Step 4.3.3.1
Divide by .