Finite Math Examples

Solve for x 50/(1+4e^(0.2t))=20
Step 1
Multiply both sides by .
Step 2
Simplify.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Cancel the common factor of .
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Step 2.1.1.1
Cancel the common factor.
Step 2.1.1.2
Rewrite the expression.
Step 2.2
Simplify the right side.
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Step 2.2.1
Simplify .
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Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Multiply.
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Step 2.2.1.2.1
Multiply by .
Step 2.2.1.2.2
Multiply by .
Step 3
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
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Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Subtract from .
Step 3.3
Divide each term in by and simplify.
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Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Cancel the common factor of .
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Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
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Step 3.3.3.1
Cancel the common factor of and .
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Step 3.3.3.1.1
Factor out of .
Step 3.3.3.1.2
Cancel the common factors.
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Step 3.3.3.1.2.1
Factor out of .
Step 3.3.3.1.2.2
Cancel the common factor.
Step 3.3.3.1.2.3
Rewrite the expression.
Step 3.4
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 3.5
Expand the left side.
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Step 3.5.1
Expand by moving outside the logarithm.
Step 3.5.2
The natural logarithm of is .
Step 3.5.3
Multiply by .
Step 3.6
Divide each term in by and simplify.
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Step 3.6.1
Divide each term in by .
Step 3.6.2
Simplify the left side.
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Step 3.6.2.1
Cancel the common factor of .
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Step 3.6.2.1.1
Cancel the common factor.
Step 3.6.2.1.2
Divide by .
Step 3.6.3
Simplify the right side.
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Step 3.6.3.1
Replace with an approximation.
Step 3.6.3.2
Divide by .
Step 3.6.3.3
Log base of is approximately .
Step 3.6.3.4
Divide by .