Precalculus Examples

Solve for x e^(3x)=3e^x
Step 1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2
Expand the left side.
Tap for more steps...
Step 2.1
Expand by moving outside the logarithm.
Step 2.2
The natural logarithm of is .
Step 2.3
Multiply by .
Step 3
Expand the right side.
Tap for more steps...
Step 3.1
Rewrite as .
Step 3.2
Expand by moving outside the logarithm.
Step 3.3
The natural logarithm of is .
Step 3.4
Multiply by .
Step 4
Move all terms containing to the left side of the equation.
Tap for more steps...
Step 4.1
Subtract from both sides of the equation.
Step 4.2
Subtract from .
Step 5
Divide each term in by and simplify.
Tap for more steps...
Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
Tap for more steps...
Step 5.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Divide by .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: