Use the quotient property of logarithms, .

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

Simplify the left side.

Exponentiation and log are inverse functions.

Factor out of .

Rewrite as .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.

Multiply both sides of the equation by .

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply.

Multiply by .

Multiply by .

Multiply by .

Subtract from 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 .

Simplify each term.

Move the negative in front of the fraction.

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 -3x-1- natural log of 7=2