Finite Math Examples

Solve for x log base 5 of x-1+ log base 5 of x+119=4
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
Rewrite as .
Step 1.3.1.4
Multiply by .
Step 1.3.2
Subtract from .
Step 2
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 3
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Raise to the power of .
Step 3.3
Subtract from both sides of the equation.
Step 3.4
Subtract from .
Step 3.5
Factor using the AC method.
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Step 3.5.1
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 3.5.2
Write the factored form using these integers.
Step 3.6
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.7
Set equal to and solve for .
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Step 3.7.1
Set equal to .
Step 3.7.2
Add to both sides of the equation.
Step 3.8
Set equal to and solve for .
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Step 3.8.1
Set equal to .
Step 3.8.2
Subtract from both sides of the equation.
Step 3.9
The final solution is all the values that make true.
Step 4
Exclude the solutions that do not make true.