Calculus Examples

Solve for x t=-5 log of 5-x/5
Step 1
Rewrite the equation as .
Step 2
Divide each term in by and simplify.
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Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Divide by .
Step 2.3
Simplify the right side.
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Step 2.3.1
Move the negative in front of the fraction.
Step 3
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 4
Solve for .
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Step 4.1
Rewrite the equation as .
Step 4.2
Subtract from both sides of the equation.
Step 4.3
Multiply both sides of the equation by .
Step 4.4
Simplify both sides of the equation.
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Step 4.4.1
Simplify the left side.
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Step 4.4.1.1
Simplify .
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Step 4.4.1.1.1
Cancel the common factor of .
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Step 4.4.1.1.1.1
Move the leading negative in into the numerator.
Step 4.4.1.1.1.2
Factor out of .
Step 4.4.1.1.1.3
Cancel the common factor.
Step 4.4.1.1.1.4
Rewrite the expression.
Step 4.4.1.1.2
Multiply.
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Step 4.4.1.1.2.1
Multiply by .
Step 4.4.1.1.2.2
Multiply by .
Step 4.4.2
Simplify the right side.
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Step 4.4.2.1
Simplify .
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Step 4.4.2.1.1
Apply the distributive property.
Step 4.4.2.1.2
Multiply by .