Trigonometry Examples

Solve for x 2 log base 3 of x- log base 3 of x+6=1
Step 1
Move all the terms containing a logarithm to the left side of the equation.
Step 2
Simplify the left side.
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Step 2.1
Simplify .
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Step 2.1.1
Simplify by moving inside the logarithm.
Step 2.1.2
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
Apply the distributive property.
Step 5.2
Multiply by .
Step 6
Subtract from both sides of the equation.
Step 7
Factor out of .
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Step 7.1
Factor out of .
Step 7.2
Factor out of .
Step 7.3
Factor out of .
Step 8
Simplify .
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Step 8.1
Apply the distributive property.
Step 8.2
Simplify the expression.
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Step 8.2.1
Multiply by .
Step 8.2.2
Move to the left of .
Step 9
Subtract from both sides of the equation.
Step 10
Factor using the AC method.
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Step 10.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 10.2
Write the factored form using these integers.
Step 11
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 12
Set equal to and solve for .
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Step 12.1
Set equal to .
Step 12.2
Add to both sides of the equation.
Step 13
Set equal to and solve for .
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Step 13.1
Set equal to .
Step 13.2
Subtract from both sides of the equation.
Step 14
The final solution is all the values that make true.
Step 15
Exclude the solutions that do not make true.