Finite Math Examples

Solve for n 120=7700(0.003/((1.003)^n-1))
Step 1
Rewrite the equation as .
Step 2
Multiply .
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Step 2.1
Combine and .
Step 2.2
Multiply by .
Step 3
Multiply both sides by .
Step 4
Simplify.
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Step 4.1
Simplify the left side.
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Step 4.1.1
Cancel the common factor of .
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Step 4.1.1.1
Cancel the common factor.
Step 4.1.1.2
Rewrite the expression.
Step 4.2
Simplify the right side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Apply the distributive property.
Step 4.2.1.2
Multiply by .
Step 5
Solve for .
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Step 5.1
Rewrite the equation as .
Step 5.2
Move all terms not containing to the right side of the equation.
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Step 5.2.1
Add to both sides of the equation.
Step 5.2.2
Add and .
Step 5.3
Divide each term in by and simplify.
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Step 5.3.1
Divide each term in by .
Step 5.3.2
Simplify the left side.
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Step 5.3.2.1
Cancel the common factor of .
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Step 5.3.2.1.1
Cancel the common factor.
Step 5.3.2.1.2
Divide by .
Step 5.3.3
Simplify the right side.
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Step 5.3.3.1
Divide by .
Step 5.4
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 5.5
Expand by moving outside the logarithm.
Step 5.6
Divide each term in by and simplify.
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Step 5.6.1
Divide each term in by .
Step 5.6.2
Simplify the left side.
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Step 5.6.2.1
Cancel the common factor of .
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Step 5.6.2.1.1
Cancel the common factor.
Step 5.6.2.1.2
Divide by .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: