Precalculus Examples

Solve for x 50/(1+e^(-x))=4
Step 1
Multiply both sides by .
Step 2
Simplify.
Tap for more steps...
Step 2.1
Simplify the left side.
Tap for more steps...
Step 2.1.1
Cancel the common factor of .
Tap for more steps...
Step 2.1.1.1
Cancel the common factor.
Step 2.1.1.2
Rewrite the expression.
Step 2.2
Simplify the right side.
Tap for more steps...
Step 2.2.1
Simplify .
Tap for more steps...
Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Multiply by .
Step 3
Solve for .
Tap for more steps...
Step 3.1
Rewrite the equation as .
Step 3.2
Move all terms not containing to the right side of the equation.
Tap for more steps...
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.
Tap for more steps...
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Tap for more steps...
Step 3.3.2.1
Cancel the common factor of .
Tap for more steps...
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.
Tap for more steps...
Step 3.3.3.1
Cancel the common factor of and .
Tap for more steps...
Step 3.3.3.1.1
Factor out of .
Step 3.3.3.1.2
Cancel the common factors.
Tap for more steps...
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.
Tap for more steps...
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.
Tap for more steps...
Step 3.6.1
Divide each term in by .
Step 3.6.2
Simplify the left side.
Tap for more steps...
Step 3.6.2.1
Dividing two negative values results in a positive value.
Step 3.6.2.2
Divide by .
Step 3.6.3
Simplify the right side.
Tap for more steps...
Step 3.6.3.1
Move the negative one from the denominator of .
Step 3.6.3.2
Rewrite as .
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: