Trigonometry Examples

Solve for x log of 2x^2=8
Step 1
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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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.
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Step 2.2.3.1
Raise to the power of .
Step 2.2.3.2
Divide by .
Step 2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.4
Simplify .
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Step 2.4.1
Rewrite as .
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Step 2.4.1.1
Factor out of .
Step 2.4.1.2
Rewrite as .
Step 2.4.2
Pull terms out from under the radical.
Step 2.5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.5.1
First, use the positive value of the to find the first solution.
Step 2.5.2
Next, use the negative value of the to find the second solution.
Step 2.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3
The result can be shown in multiple forms.
Exact Form:
Decimal Form: