Finite Math Examples

Solve for x log of 7x+4- log of x-5=1
Step 1
Use the quotient property of logarithms, .
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
Cross multiply to remove the fraction.
Step 4
Simplify .
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Step 4.1
Apply the distributive property.
Step 4.2
Multiply by .
Step 5
Move all terms containing to the left side of the equation.
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Step 5.1
Subtract from both sides of the equation.
Step 5.2
Subtract from .
Step 6
Move all terms not containing to the right side of the equation.
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Step 6.1
Subtract from both sides of the equation.
Step 6.2
Subtract from .
Step 7
Divide each term in by and simplify.
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Step 7.1
Divide each term in by .
Step 7.2
Simplify the left side.
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Step 7.2.1
Cancel the common factor of .
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Step 7.2.1.1
Cancel the common factor.
Step 7.2.1.2
Divide by .
Step 7.3
Simplify the right side.
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Step 7.3.1
Divide by .