Calculus Examples

Solve for x natural log of x- natural log of x^2+ natural log of 3=0
Step 1
Simplify the left side.
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Step 1.1
Use the quotient property of logarithms, .
Step 1.2
Use the product property of logarithms, .
Step 1.3
Cancel the common factor of and .
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Step 1.3.1
Raise to the power of .
Step 1.3.2
Factor out of .
Step 1.3.3
Cancel the common factors.
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Step 1.3.3.1
Factor out of .
Step 1.3.3.2
Cancel the common factor.
Step 1.3.3.3
Rewrite the expression.
Step 1.4
Combine and .
Step 2
To solve for , rewrite the equation using properties of logarithms.
Step 3
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 4
Solve for .
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Step 4.1
Rewrite the equation as .
Step 4.2
Anything raised to is .
Step 4.3
Find the LCD of the terms in the equation.
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Step 4.3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 4.3.2
The LCM of one and any expression is the expression.
Step 4.4
Multiply each term in by to eliminate the fractions.
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Step 4.4.1
Multiply each term in by .
Step 4.4.2
Simplify the left side.
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Step 4.4.2.1
Cancel the common factor of .
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Step 4.4.2.1.1
Cancel the common factor.
Step 4.4.2.1.2
Rewrite the expression.
Step 4.4.3
Simplify the right side.
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Step 4.4.3.1
Multiply by .
Step 4.5
Rewrite the equation as .