Precalculus Examples

Solve for x 1000e^(-4x)=75
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Cancel the common factor of .
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Step 1.2.1.1
Cancel the common factor.
Step 1.2.1.2
Divide by .
Step 1.3
Simplify the right side.
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Step 1.3.1
Cancel the common factor of and .
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Step 1.3.1.1
Factor out of .
Step 1.3.1.2
Cancel the common factors.
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Step 1.3.1.2.1
Factor out of .
Step 1.3.1.2.2
Cancel the common factor.
Step 1.3.1.2.3
Rewrite the expression.
Step 2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 3
Expand the left side.
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Step 3.1
Expand by moving outside the logarithm.
Step 3.2
The natural logarithm of is .
Step 3.3
Multiply by .
Step 4
Divide each term in by and simplify.
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Step 4.1
Divide each term in by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Cancel the common factor of .
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Step 4.2.1.1
Cancel the common factor.
Step 4.2.1.2
Divide by .
Step 4.3
Simplify the right side.
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Step 4.3.1
Move the negative in front of the fraction.
Step 5
The result can be shown in multiple forms.
Exact Form:
Decimal Form: