Finite Math Examples

Solve for x 5^(2x)+5^(x+1)-24=0
Step 1
Factor the left side of the equation.
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Step 1.1
Rewrite as .
Step 1.2
Rewrite as .
Step 1.3
Let . Substitute for all occurrences of .
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Step 1.3.1
Evaluate the exponent.
Step 1.3.2
Move to the left of .
Step 1.4
Factor using the AC method.
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Step 1.4.1
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 1.4.2
Write the factored form using these integers.
Step 1.5
Replace all occurrences of with .
Step 2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3
Set equal to and solve for .
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Step 3.1
Set equal to .
Step 3.2
Solve for .
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Step 3.2.1
Add to both sides of the equation.
Step 3.2.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 3.2.3
Expand by moving outside the logarithm.
Step 3.2.4
Divide each term in by and simplify.
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Step 3.2.4.1
Divide each term in by .
Step 3.2.4.2
Simplify the left side.
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Step 3.2.4.2.1
Cancel the common factor of .
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Step 3.2.4.2.1.1
Cancel the common factor.
Step 3.2.4.2.1.2
Divide by .
Step 4
Set equal to and solve for .
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Step 4.1
Set equal to .
Step 4.2
Solve for .
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Step 4.2.1
Subtract from both sides of the equation.
Step 4.2.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 4.2.3
The equation cannot be solved because is undefined.
Undefined
Step 4.2.4
There is no solution for
No solution
No solution
No solution
Step 5
The final solution is all the values that make true.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: