Pre-Algebra Examples

Solve for x 2^(2x)-2^(x-1)-2^2+2<0
Step 1
Rewrite as .
Step 2
Rewrite as exponentiation.
Step 3
Remove parentheses.
Step 4
Substitute for .
Step 5
Simplify each term.
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Step 5.1
Rewrite the expression using the negative exponent rule .
Step 5.2
Combine and .
Step 5.3
Raise to the power of .
Step 5.4
Multiply by .
Step 6
Add and .
Step 7
Solve for .
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Step 7.1
Multiply through by the least common denominator , then simplify.
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Step 7.1.1
Apply the distributive property.
Step 7.1.2
Simplify.
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Step 7.1.2.1
Cancel the common factor of .
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Step 7.1.2.1.1
Move the leading negative in into the numerator.
Step 7.1.2.1.2
Cancel the common factor.
Step 7.1.2.1.3
Rewrite the expression.
Step 7.1.2.2
Multiply by .
Step 7.2
Use the quadratic formula to find the solutions.
Step 7.3
Substitute the values , , and into the quadratic formula and solve for .
Step 7.4
Simplify.
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Step 7.4.1
Simplify the numerator.
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Step 7.4.1.1
Raise to the power of .
Step 7.4.1.2
Multiply .
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Step 7.4.1.2.1
Multiply by .
Step 7.4.1.2.2
Multiply by .
Step 7.4.1.3
Add and .
Step 7.4.2
Multiply by .
Step 7.5
The final answer is the combination of both solutions.
Step 8
Substitute for in .
Step 9
Solve .
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Step 9.1
Rewrite the equation as .
Step 9.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 9.3
Expand by moving outside the logarithm.
Step 9.4
Divide each term in by and simplify.
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Step 9.4.1
Divide each term in by .
Step 9.4.2
Simplify the left side.
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Step 9.4.2.1
Cancel the common factor of .
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Step 9.4.2.1.1
Cancel the common factor.
Step 9.4.2.1.2
Divide by .
Step 10
Substitute for in .
Step 11
Solve .
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Step 11.1
Rewrite the equation as .
Step 11.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 11.3
The equation cannot be solved because is undefined.
Undefined
Step 11.4
There is no solution for
No solution
No solution
Step 12
List the solutions that makes the equation true.
Step 13
The solution consists of all of the true intervals.
Step 14
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 15