Enter a problem...
Finite Math Examples
Step 1
Move all the terms containing a logarithm to the left side of the equation.
Step 2
Step 2.1
Simplify .
Step 2.1.1
Simplify by moving inside the logarithm.
Step 2.1.2
Use the quotient property of logarithms, .
Step 2.1.3
Use the quotient property of logarithms, .
Step 2.1.4
Multiply the numerator by the reciprocal of the denominator.
Step 2.1.5
Combine.
Step 2.1.6
Multiply.
Step 2.1.6.1
Multiply by .
Step 2.1.6.2
Multiply by .
Step 3
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Step 4
Step 4.1
Rewrite the equation as .
Step 4.2
Multiply both sides of the equation by .
Step 4.3
Simplify both sides of the equation.
Step 4.3.1
Simplify the left side.
Step 4.3.1.1
Cancel the common factor of .
Step 4.3.1.1.1
Cancel the common factor.
Step 4.3.1.1.2
Rewrite the expression.
Step 4.3.2
Simplify the right side.
Step 4.3.2.1
Move the decimal point in to the left by places and increase the power of by .
Step 4.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.5
Simplify .
Step 4.5.1
Rewrite as .
Step 4.5.2
Evaluate the root.
Step 4.5.3
Pull terms out from under the radical, assuming positive real numbers.
Step 4.5.4
Raise to the power of .
Step 4.6
The complete solution is the result of both the positive and negative portions of the solution.
Step 4.6.1
First, use the positive value of the to find the first solution.
Step 4.6.2
Next, use the negative value of the to find the second solution.
Step 4.6.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 5
Exclude the solutions that do not make true.
Step 6
The result can be shown in multiple forms.
Scientific Notation:
Expanded Form: