Finite Math Examples

Solve for x natural log of 3x+10- natural log of x = natural log of 4
Step 1
Use the quotient property of logarithms, .
Step 2
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Step 3
Solve for .
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Step 3.1
Find the LCD of the terms in the equation.
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Step 3.1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.1.2
The LCM of one and any expression is the expression.
Step 3.2
Multiply each term in by to eliminate the fractions.
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Step 3.2.1
Multiply each term in by .
Step 3.2.2
Simplify the left side.
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Step 3.2.2.1
Cancel the common factor of .
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Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Rewrite the expression.
Step 3.3
Solve the equation.
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Step 3.3.1
Move all terms containing to the left side of the equation.
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Step 3.3.1.1
Subtract from both sides of the equation.
Step 3.3.1.2
Subtract from .
Step 3.3.2
Subtract from both sides of the equation.
Step 3.3.3
Divide each term in by and simplify.
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Step 3.3.3.1
Divide each term in by .
Step 3.3.3.2
Simplify the left side.
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Step 3.3.3.2.1
Dividing two negative values results in a positive value.
Step 3.3.3.2.2
Divide by .
Step 3.3.3.3
Simplify the right side.
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Step 3.3.3.3.1
Divide by .