Finite Math Examples

Determine if Linear log base g of x-12+ log base g of x=2
Step 1
Solve the equation for .
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Step 1.1
Simplify the left side.
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Step 1.1.1
Use the product property of logarithms, .
Step 1.1.2
Apply the distributive property.
Step 1.1.3
Multiply by .
Step 1.2
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 1.3
Solve for .
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Step 1.3.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 1.3.2
Factor out of .
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Step 1.3.2.1
Factor out of .
Step 1.3.2.2
Factor out of .
Step 1.3.2.3
Factor out of .
Step 1.3.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 1.3.3.1
First, use the positive value of the to find the first solution.
Step 1.3.3.2
Next, use the negative value of the to find the second solution.
Step 1.3.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2
A linear equation is an equation of a straight line, which means that the degree of a linear equation must be or for each of its variables. In this case, the degree of the variable in the equation violates the linear equation definition, which means that the equation is not a linear equation.
Not Linear