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

Math
Simplify the left side.
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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 .
Solve for
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Take the root of both sides of the to eliminate the exponent on the left side.
Simplify .
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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

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