Use the product property of logarithms, .

Multiply by .

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

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

Simplify .

Rewrite as .

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

Verify each of the solutions by substituting them into and solving.

Solve for x log base x of 100+ log base x of 1000=5