Trigonometry Examples

Solve for x natural log of 5x- natural log of x+2 = natural log of 8
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
Remove parentheses.
Step 3.1.3
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 3.2.3
Simplify the right side.
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Step 3.2.3.1
Apply the distributive property.
Step 3.2.3.2
Multiply by .
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
Divide each term in by and simplify.
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Step 3.3.2.1
Divide each term in by .
Step 3.3.2.2
Simplify the left side.
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Step 3.3.2.2.1
Cancel the common factor of .
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Step 3.3.2.2.1.1
Cancel the common factor.
Step 3.3.2.2.1.2
Divide by .
Step 3.3.2.3
Simplify the right side.
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Step 3.3.2.3.1
Move the negative in front of the fraction.
Step 4
Exclude the solutions that do not make true.