Algebra Examples

Solve for x 12e^(2x)-5=17e^x
Step 1
Subtract from both sides of the equation.
Step 2
Rewrite as exponentiation.
Step 3
Substitute for .
Step 4
Move .
Step 5
Solve for .
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Step 5.1
Factor by grouping.
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Step 5.1.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 5.1.1.1
Factor out of .
Step 5.1.1.2
Rewrite as plus
Step 5.1.1.3
Apply the distributive property.
Step 5.1.2
Factor out the greatest common factor from each group.
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Step 5.1.2.1
Group the first two terms and the last two terms.
Step 5.1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 5.1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 5.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 5.3
Set equal to and solve for .
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Step 5.3.1
Set equal to .
Step 5.3.2
Solve for .
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Step 5.3.2.1
Subtract from both sides of the equation.
Step 5.3.2.2
Divide each term in by and simplify.
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Step 5.3.2.2.1
Divide each term in by .
Step 5.3.2.2.2
Simplify the left side.
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Step 5.3.2.2.2.1
Cancel the common factor of .
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Step 5.3.2.2.2.1.1
Cancel the common factor.
Step 5.3.2.2.2.1.2
Divide by .
Step 5.3.2.2.3
Simplify the right side.
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Step 5.3.2.2.3.1
Move the negative in front of the fraction.
Step 5.4
Set equal to and solve for .
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Step 5.4.1
Set equal to .
Step 5.4.2
Solve for .
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Step 5.4.2.1
Add to both sides of the equation.
Step 5.4.2.2
Divide each term in by and simplify.
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Step 5.4.2.2.1
Divide each term in by .
Step 5.4.2.2.2
Simplify the left side.
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Step 5.4.2.2.2.1
Cancel the common factor of .
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Step 5.4.2.2.2.1.1
Cancel the common factor.
Step 5.4.2.2.2.1.2
Divide by .
Step 5.5
The final solution is all the values that make true.
Step 6
Substitute for in .
Step 7
Solve .
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Step 7.1
Rewrite the equation as .
Step 7.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 7.3
The equation cannot be solved because is undefined.
Undefined
Step 7.4
There is no solution for
No solution
No solution
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 the left side.
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Step 9.3.1
Expand by moving outside the logarithm.
Step 9.3.2
The natural logarithm of is .
Step 9.3.3
Multiply by .
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: