# Solve for x log base 9 of x+ log base 9 of 8x-1=1

Simplify the left side.
Use the product property of logarithms, .
Simplify by multiplying through.
Apply the distributive property.
Reorder.
Rewrite using the commutative property of multiplication.
Move to the left of .
Simplify each term.
Multiply by by adding the exponents.
Move .
Multiply by .
Rewrite as .
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for
Evaluate the exponent.
Rewrite the equation as .
Move to the left side of the equation by subtracting it from both sides.
Factor by grouping.
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
Factor out of .
Rewrite as plus
Apply the distributive property.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
Factor out the greatest common factor (GCF) from each group.
Factor the polynomial by factoring out the greatest common factor, .
Set equal to and solve for .
Set the factor equal to .
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 .
Set equal to and solve for .
Set the factor equal to .
Subtract from both sides of the equation.
The solution is the result of and .
Exclude the solutions that do not make true.
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form:
Solve for x log base 9 of x+ log base 9 of 8x-1=1