Precalculus Examples

Solve for x natural log of x+9+ natural log of x-9=0
Step 1
Simplify the left side.
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Step 1.1
Use the product property of logarithms, .
Step 1.2
Expand using the FOIL Method.
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Step 1.2.1
Apply the distributive property.
Step 1.2.2
Apply the distributive property.
Step 1.2.3
Apply the distributive property.
Step 1.3
Simplify terms.
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Step 1.3.1
Combine the opposite terms in .
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Step 1.3.1.1
Reorder the factors in the terms and .
Step 1.3.1.2
Add and .
Step 1.3.1.3
Add and .
Step 1.3.2
Simplify each term.
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Step 1.3.2.1
Multiply by .
Step 1.3.2.2
Multiply by .
Step 2
To solve for , rewrite the equation using properties of logarithms.
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
Anything raised to is .
Step 4.3
Move all terms not containing to the right side of the equation.
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Step 4.3.1
Add to both sides of the equation.
Step 4.3.2
Add and .
Step 4.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 4.5.1
First, use the positive value of the to find the first solution.
Step 4.5.2
Next, use the negative value of the to find the second solution.
Step 4.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: