Precalculus Examples

Solve for x 2 log of x = log of 2+ log of 6x-10
Step 1
Simplify the left side.
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Step 1.1
Simplify by moving inside the logarithm.
Step 2
Simplify the right side.
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Step 2.1
Simplify .
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Step 2.1.1
Use the product property of logarithms, .
Step 2.1.2
Apply the distributive property.
Step 2.1.3
Multiply.
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Step 2.1.3.1
Multiply by .
Step 2.1.3.2
Multiply by .
Step 3
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
Step 4
Solve for .
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Step 4.1
Subtract from both sides of the equation.
Step 4.2
Add to both sides of the equation.
Step 4.3
Factor using the AC method.
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Step 4.3.1
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 4.3.2
Write the factored form using these integers.
Step 4.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.5
Set equal to and solve for .
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Step 4.5.1
Set equal to .
Step 4.5.2
Add to both sides of the equation.
Step 4.6
Set equal to and solve for .
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Step 4.6.1
Set equal to .
Step 4.6.2
Add to both sides of the equation.
Step 4.7
The final solution is all the values that make true.