Basic Math Examples

Solve for n 56=(1-(1+0.015)^(-n))/0.015
Step 1
Rewrite the equation as .
Step 2
Multiply both sides by .
Step 3
Simplify.
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Step 3.1
Simplify the left side.
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Step 3.1.1
Simplify .
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Step 3.1.1.1
Add and .
Step 3.1.1.2
Cancel the common factor of .
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Step 3.1.1.2.1
Cancel the common factor.
Step 3.1.1.2.2
Rewrite the expression.
Step 3.2
Simplify the right side.
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Step 3.2.1
Multiply by .
Step 4
Solve for .
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Step 4.1
Move all terms not containing to the right side of the equation.
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Step 4.1.1
Subtract from both sides of the equation.
Step 4.1.2
Subtract from .
Step 4.2
Divide each term in by and simplify.
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Step 4.2.1
Divide each term in by .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Dividing two negative values results in a positive value.
Step 4.2.2.2
Divide by .
Step 4.2.3
Simplify the right side.
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Step 4.2.3.1
Divide by .
Step 4.3
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 4.4
Expand by moving outside the logarithm.
Step 4.5
Divide each term in by and simplify.
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Step 4.5.1
Divide each term in by .
Step 4.5.2
Simplify the left side.
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Step 4.5.2.1
Dividing two negative values results in a positive value.
Step 4.5.2.2
Cancel the common factor of .
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Step 4.5.2.2.1
Cancel the common factor.
Step 4.5.2.2.2
Divide by .
Step 4.5.3
Simplify the right side.
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Step 4.5.3.1
Move the negative in front of the fraction.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: