Trigonometry Examples

Solve for x log of 5x-1=2+ log of x-2
Step 1
Move all the terms containing a logarithm to the left side of the equation.
Step 2
Use the quotient property 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
Cross multiply to remove the fraction.
Step 5
Simplify .
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Step 5.1
Raise to the power of .
Step 5.2
Apply the distributive property.
Step 5.3
Multiply by .
Step 6
Move all terms containing to the left 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
Move all terms not containing to the right side of the equation.
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Step 7.1
Add to both sides of the equation.
Step 7.2
Add and .
Step 8
Divide each term in by and simplify.
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Step 8.1
Divide each term in by .
Step 8.2
Simplify the left side.
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Step 8.2.1
Cancel the common factor of .
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Step 8.2.1.1
Cancel the common factor.
Step 8.2.1.2
Divide by .
Step 8.3
Simplify the right side.
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Step 8.3.1
Dividing two negative values results in a positive value.
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: