Use the quotient property of logarithms, .

To solve for , rewrite the equation using properties of logarithms.

Exponentiation and log are inverse functions.

Simplify.

Solve for .

Multiply each term by and simplify.

Multiply each term in by .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Simplify by multiplying through.

Apply the distributive property.

Move to the left of .

Move to the left of .

Rewrite the equation as .

Subtract from both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Simplify the left side of the equation by cancelling the common factors.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Cancel the common factor.

Divide by .

Simplify each term.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x natural log of 2- natural log of 3x+2=1