Precalculus Examples

Solve for x 7e^x=6-e^(-x)
Step 1
Add to both sides of the equation.
Step 2
Rewrite as exponentiation.
Step 3
Substitute for .
Step 4
Rewrite the expression using the negative exponent rule .
Step 5
Solve for .
Tap for more steps...
Step 5.1
Find the LCD of the terms in the equation.
Tap for more steps...
Step 5.1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 5.1.2
The LCM of one and any expression is the expression.
Step 5.2
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 5.2.1
Multiply each term in by .
Step 5.2.2
Simplify the left side.
Tap for more steps...
Step 5.2.2.1
Simplify each term.
Tap for more steps...
Step 5.2.2.1.1
Multiply by by adding the exponents.
Tap for more steps...
Step 5.2.2.1.1.1
Move .
Step 5.2.2.1.1.2
Multiply by .
Step 5.2.2.1.2
Cancel the common factor of .
Tap for more steps...
Step 5.2.2.1.2.1
Cancel the common factor.
Step 5.2.2.1.2.2
Rewrite the expression.
Step 5.3
Solve the equation.
Tap for more steps...
Step 5.3.1
Subtract from both sides of the equation.
Step 5.3.2
Use the quadratic formula to find the solutions.
Step 5.3.3
Substitute the values , , and into the quadratic formula and solve for .
Step 5.3.4
Simplify.
Tap for more steps...
Step 5.3.4.1
Simplify the numerator.
Tap for more steps...
Step 5.3.4.1.1
Raise to the power of .
Step 5.3.4.1.2
Multiply .
Tap for more steps...
Step 5.3.4.1.2.1
Multiply by .
Step 5.3.4.1.2.2
Multiply by .
Step 5.3.4.1.3
Subtract from .
Step 5.3.4.1.4
Rewrite as .
Tap for more steps...
Step 5.3.4.1.4.1
Factor out of .
Step 5.3.4.1.4.2
Rewrite as .
Step 5.3.4.1.5
Pull terms out from under the radical.
Step 5.3.4.2
Multiply by .
Step 5.3.4.3
Simplify .
Step 5.3.5
The final answer is the combination of both solutions.
Step 6
Substitute for in .
Step 7
Solve .
Tap for more steps...
Step 7.1
Rewrite the equation as .
Step 7.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 7.3
Expand the left side.
Tap for more steps...
Step 7.3.1
Expand by moving outside the logarithm.
Step 7.3.2
The natural logarithm of is .
Step 7.3.3
Multiply by .
Step 8
Substitute for in .
Step 9
Solve .
Tap for more steps...
Step 9.1
Rewrite the equation as .
Step 9.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 9.3
Expand the left side.
Tap for more steps...
Step 9.3.1
Expand by moving outside the logarithm.
Step 9.3.2
The natural logarithm of is .
Step 9.3.3
Multiply by .
Step 10
List the solutions that makes the equation true.
Step 11
The result can be shown in multiple forms.
Exact Form:
Decimal Form: