Precalculus Examples

Solve for x natural log of x-6+ natural log of x+7=1
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 and combine like terms.
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Step 1.3.1
Simplify each term.
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Step 1.3.1.1
Multiply by .
Step 1.3.1.2
Move to the left of .
Step 1.3.1.3
Multiply by .
Step 1.3.2
Subtract from .
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
Subtract from both sides of the equation.
Step 4.3
Use the quadratic formula to find the solutions.
Step 4.4
Substitute the values , , and into the quadratic formula and solve for .
Step 4.5
Simplify.
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Step 4.5.1
Simplify the numerator.
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Step 4.5.1.1
One to any power is one.
Step 4.5.1.2
Multiply by .
Step 4.5.1.3
Apply the distributive property.
Step 4.5.1.4
Multiply by .
Step 4.5.1.5
Multiply by .
Step 4.5.1.6
Add and .
Step 4.5.2
Multiply by .
Step 4.6
The final answer is the combination of both solutions.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: