Pre-Algebra Examples

Solve for x 2^(2x+2)*3^(x+1)=14
Step 1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2
Expand the left side.
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Step 2.1
Rewrite as .
Step 2.2
Expand by moving outside the logarithm.
Step 2.3
Expand by moving outside the logarithm.
Step 3
Simplify the left side.
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Step 3.1
Simplify each term.
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Step 3.1.1
Apply the distributive property.
Step 3.1.2
Apply the distributive property.
Step 3.1.3
Multiply by .
Step 4
Move .
Step 5
Move all the terms containing a logarithm to the left side of the equation.
Step 6
Use the quotient property of logarithms, .
Step 7
Move all terms not containing to the right side of the equation.
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Step 7.1
Subtract from both sides of the equation.
Step 7.2
Subtract from both sides of the equation.
Step 8
Factor out of .
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Step 8.1
Factor out of .
Step 8.2
Factor out of .
Step 8.3
Factor out of .
Step 9
Divide each term in by and simplify.
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Step 9.1
Divide each term in by .
Step 9.2
Simplify the left side.
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Step 9.2.1
Cancel the common factor of .
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Step 9.2.1.1
Cancel the common factor.
Step 9.2.1.2
Divide by .
Step 9.3
Simplify the right side.
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Step 9.3.1
Simplify each term.
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Step 9.3.1.1
Move the negative in front of the fraction.
Step 9.3.1.2
Move the negative in front of the fraction.
Step 9.3.2
Simplify terms.
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Step 9.3.2.1
Combine the numerators over the common denominator.
Step 9.3.2.2
Factor out of .
Step 9.3.2.3
Factor out of .
Step 9.3.2.4
Factor out of .
Step 9.3.2.5
Simplify the expression.
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Step 9.3.2.5.1
Rewrite as .
Step 9.3.2.5.2
Move the negative in front of the fraction.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: