Trigonometry Examples

Solve for x natural log of x^2-5 = natural log of 4x
Step 1
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Step 2
Solve for .
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Factor using the AC method.
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Step 2.2.1
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 2.2.2
Write the factored form using these integers.
Step 2.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.4
Set equal to and solve for .
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Step 2.4.1
Set equal to .
Step 2.4.2
Add to both sides of the equation.
Step 2.5
Set equal to and solve for .
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Step 2.5.1
Set equal to .
Step 2.5.2
Subtract from both sides of the equation.
Step 2.6
The final solution is all the values that make true.
Step 3
Exclude the solutions that do not make true.