Use the product property of logarithms, .

Use the quotient property of logarithms, .

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

Subtract from both sides of the equation.

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .

The LCM is the smallest number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

The number is not a prime number because it only has one positive factor, which is itself.

Not prime

The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.

The factor for is itself.

occurs time.

The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either term.

Multiply each term by and simplify.

Multiply each term in by in order to remove all the denominators from the equation.

Simplify each term.

Multiply by by adding the exponents.

Move .

Multiply by .

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Multiply by .

Solve the equation.

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Take the root of both sides of the to eliminate the exponent on the left side.

The complete solution is the result of both the positive and negative portions of the solution.

Simplify the right side of the equation.

Rewrite as .

Simplify the denominator.

Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the to find the first solution.

Next, use the negative value of the to find the second solution.

The complete solution is the result of both the positive and negative portions of the solution.

Exclude the solutions that do not make true.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x log of 4+ log of x = log of 5- log of x