Finite Math Examples

Solve for b log base b of x=1/2* log base b of 4+2/3* log base b of 125- log base b of 10
Step 1
Simplify the right side.
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Step 1.1
Simplify each term.
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Step 1.1.1
Combine and .
Step 1.1.2
Combine and .
Step 2
Multiply each term in by to eliminate the fractions.
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Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Move to the left of .
Step 2.3
Simplify the right side.
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Step 2.3.1
Simplify each term.
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Step 2.3.1.1
Cancel the common factor of .
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Step 2.3.1.1.1
Factor out of .
Step 2.3.1.1.2
Cancel the common factor.
Step 2.3.1.1.3
Rewrite the expression.
Step 2.3.1.2
Move to the left of .
Step 2.3.1.3
Cancel the common factor of .
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Step 2.3.1.3.1
Factor out of .
Step 2.3.1.3.2
Cancel the common factor.
Step 2.3.1.3.3
Rewrite the expression.
Step 2.3.1.4
Multiply by .
Step 2.3.1.5
Multiply by .
Step 3
Simplify the left side.
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Step 3.1
Simplify by moving inside the logarithm.
Step 4
Simplify the right side.
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Step 4.1
Simplify .
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Step 4.1.1
Simplify each term.
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Step 4.1.1.1
Simplify by moving inside the logarithm.
Step 4.1.1.2
Raise to the power of .
Step 4.1.1.3
Simplify by moving inside the logarithm.
Step 4.1.1.4
Raise to the power of .
Step 4.1.1.5
Simplify by moving inside the logarithm.
Step 4.1.1.6
Raise to the power of .
Step 4.1.2
Use the product property of logarithms, .
Step 4.1.3
Use the quotient property of logarithms, .
Step 4.1.4
Cancel the common factor of and .
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Step 4.1.4.1
Factor out of .
Step 4.1.4.2
Cancel the common factors.
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Step 4.1.4.2.1
Factor out of .
Step 4.1.4.2.2
Cancel the common factor.
Step 4.1.4.2.3
Rewrite the expression.
Step 4.1.5
Cancel the common factor of and .
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Step 4.1.5.1
Factor out of .
Step 4.1.5.2
Cancel the common factors.
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Step 4.1.5.2.1
Factor out of .
Step 4.1.5.2.2
Cancel the common factor.
Step 4.1.5.2.3
Rewrite the expression.
Step 4.1.5.2.4
Divide by .
Step 5
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Step 6
Solve for .
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Step 6.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 6.2
Simplify .
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Step 6.2.1
Rewrite as .
Step 6.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 6.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 6.3.1
First, use the positive value of the to find the first solution.
Step 6.3.2
Next, use the negative value of the to find the second solution.
Step 6.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 7
The variable got canceled.
All real numbers
Step 8
The result can be shown in multiple forms.
All real numbers
Interval Notation: