Finite Math Examples

Solve by Factoring natural log of x+ natural log of x+1 = natural log of 6
Step 1
Subtract from both sides of the equation.
Step 2
Simplify .
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Step 2.1
Use the product property of logarithms, .
Step 2.2
Use the quotient property of logarithms, .
Step 3
To solve for , rewrite the equation using properties of logarithms.
Step 4
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 5
Solve for .
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Step 5.1
Rewrite the equation as .
Step 5.2
Multiply both sides of the equation by .
Step 5.3
Simplify both sides of the equation.
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Step 5.3.1
Simplify the left side.
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Step 5.3.1.1
Simplify .
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Step 5.3.1.1.1
Cancel the common factor of .
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Step 5.3.1.1.1.1
Cancel the common factor.
Step 5.3.1.1.1.2
Rewrite the expression.
Step 5.3.1.1.2
Apply the distributive property.
Step 5.3.1.1.3
Simplify the expression.
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Step 5.3.1.1.3.1
Multiply by .
Step 5.3.1.1.3.2
Multiply by .
Step 5.3.2
Simplify the right side.
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Step 5.3.2.1
Simplify .
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Step 5.3.2.1.1
Anything raised to is .
Step 5.3.2.1.2
Multiply by .
Step 5.4
Subtract from both sides of the equation.
Step 5.5
Factor using the AC method.
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Step 5.5.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 5.5.2
Write the factored form using these integers.
Step 5.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5.7
Set equal to and solve for .
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Step 5.7.1
Set equal to .
Step 5.7.2
Add to both sides of the equation.
Step 5.8
Set equal to and solve for .
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Step 5.8.1
Set equal to .
Step 5.8.2
Subtract from both sides of the equation.
Step 5.9
The final solution is all the values that make true.