Finite Math Examples

Solve for x natural log of x+ natural log of x-1 = natural log of 2+ natural log of 3
Step 1
Simplify the left side.
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Step 1.1
Use the product property of logarithms, .
Step 1.2
Simplify by multiplying through.
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Step 1.2.1
Apply the distributive property.
Step 1.2.2
Simplify the expression.
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Step 1.2.2.1
Multiply by .
Step 1.2.2.2
Move to the left of .
Step 1.3
Rewrite as .
Step 2
Simplify the right side.
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Step 2.1
Use the product property of logarithms, .
Step 2.2
Multiply by .
Step 3
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Step 4
Solve for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Factor using the AC method.
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Step 4.2.1
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 4.2.2
Write the factored form using these integers.
Step 4.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.4
Set equal to and solve for .
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Step 4.4.1
Set equal to .
Step 4.4.2
Add to both sides of the equation.
Step 4.5
Set equal to and solve for .
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Step 4.5.1
Set equal to .
Step 4.5.2
Subtract from both sides of the equation.
Step 4.6
The final solution is all the values that make true.
Step 5
Exclude the solutions that do not make true.