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Pre-Algebra Examples
Step 1
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2
Step 2.1
Rewrite as .
Step 2.2
Expand by moving outside the logarithm.
Step 2.3
Expand by moving outside the logarithm.
Step 3
Step 3.1
Simplify each term.
Step 3.1.1
Apply the distributive property.
Step 3.1.2
Apply the distributive property.
Step 3.1.3
Multiply by .
Step 4
Move .
Step 5
Move all the terms containing a logarithm to the left side of the equation.
Step 6
Use the quotient property of logarithms, .
Step 7
Step 7.1
Subtract from both sides of the equation.
Step 7.2
Subtract from both sides of the equation.
Step 8
Step 8.1
Factor out of .
Step 8.2
Factor out of .
Step 8.3
Factor out of .
Step 9
Step 9.1
Divide each term in by .
Step 9.2
Simplify the left side.
Step 9.2.1
Cancel the common factor of .
Step 9.2.1.1
Cancel the common factor.
Step 9.2.1.2
Divide by .
Step 9.3
Simplify the right side.
Step 9.3.1
Simplify each term.
Step 9.3.1.1
Move the negative in front of the fraction.
Step 9.3.1.2
Move the negative in front of the fraction.
Step 9.3.2
Simplify terms.
Step 9.3.2.1
Combine the numerators over the common denominator.
Step 9.3.2.2
Factor out of .
Step 9.3.2.3
Factor out of .
Step 9.3.2.4
Factor out of .
Step 9.3.2.5
Simplify the expression.
Step 9.3.2.5.1
Rewrite as .
Step 9.3.2.5.2
Move the negative in front of the fraction.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: