Use the quotient property of logarithms, .

Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .

Raise to the power of .

Rewrite the equation as .

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.

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

Subtract from .

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 .

Dividing two negative values results in a positive value.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x log base 5 of x+1- log base 5 of x=4