Trigonometry Examples

Solve for x natural log of (3x-2)^2=5
Step 1
Write in exponential form.
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Step 1.1
For logarithmic equations, is equivalent to such that , , and . In this case, , , and .
Step 1.2
Substitute the values of , , and into the equation .
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.3
Simplify .
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Step 2.3.1
Rewrite as .
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Step 2.3.1.1
Factor out .
Step 2.3.1.2
Rewrite as .
Step 2.3.2
Pull terms out from under the radical.
Step 2.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.4.1
First, use the positive value of the to find the first solution.
Step 2.4.2
Add to both sides of the equation.
Step 2.4.3
Divide each term in by and simplify.
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Step 2.4.3.1
Divide each term in by .
Step 2.4.3.2
Simplify the left side.
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Step 2.4.3.2.1
Cancel the common factor of .
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Step 2.4.3.2.1.1
Cancel the common factor.
Step 2.4.3.2.1.2
Divide by .
Step 2.4.4
Next, use the negative value of the to find the second solution.
Step 2.4.5
Add to both sides of the equation.
Step 2.4.6
Divide each term in by and simplify.
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Step 2.4.6.1
Divide each term in by .
Step 2.4.6.2
Simplify the left side.
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Step 2.4.6.2.1
Cancel the common factor of .
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Step 2.4.6.2.1.1
Cancel the common factor.
Step 2.4.6.2.1.2
Divide by .
Step 2.4.6.3
Simplify the right side.
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Step 2.4.6.3.1
Move the negative in front of the fraction.
Step 2.4.7
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: