Finite Math Examples

Solve for x log base b of 8+x- log base b of x=3 log base b of 2
Step 1
Use the quotient property of logarithms, .
Step 2
Simplify by moving inside the logarithm.
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
Raise to the power of .
Step 4.2
Find the LCD of the terms in the equation.
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Step 4.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 4.2.2
The LCM of one and any expression is the expression.
Step 4.3
Multiply each term in by to eliminate the fractions.
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Step 4.3.1
Multiply each term in by .
Step 4.3.2
Simplify the left side.
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Step 4.3.2.1
Cancel the common factor of .
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Step 4.3.2.1.1
Cancel the common factor.
Step 4.3.2.1.2
Rewrite the expression.
Step 4.4
Solve the equation.
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Step 4.4.1
Move all terms containing to the left side of the equation.
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Step 4.4.1.1
Subtract from both sides of the equation.
Step 4.4.1.2
Subtract from .
Step 4.4.2
Subtract from both sides of the equation.
Step 4.4.3
Divide each term in by and simplify.
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Step 4.4.3.1
Divide each term in by .
Step 4.4.3.2
Simplify the left side.
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Step 4.4.3.2.1
Cancel the common factor of .
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Step 4.4.3.2.1.1
Cancel the common factor.
Step 4.4.3.2.1.2
Divide by .
Step 4.4.3.3
Simplify the right side.
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Step 4.4.3.3.1
Dividing two negative values results in a positive value.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: