Question

Simplify the expressions. $$10^{-\log _{10}(1 / x)}$$

   Simplify the expressions.
$$10^{-\log _{10}(1 / x)}$$

Calculus: A Complete Course

Calculus: A Complete Course

Robert Adams ,… 9th Edition

Chapter 3, Problem 9

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Solved by Expert Dwijendra Rao

10/08/2021

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Simplify the expressions. $$10^{-\log _{10}(1 / x)}$$

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Key Concepts

Logarithmic Identity for Reciprocals

This identity states that the logarithm of the reciprocal of a number is the negative of the logarithm of the number itself, which is written as log?(1/x) = -log?(x). Leveraging this property allows for transforming and simplifying expressions that involve the logarithm of a fraction or reciprocal.

Inverse Relationship between Exponents and Logarithms

This concept highlights that exponentiation and logarithms are inverse operations. In particular, raising a base to its logarithm (with the same base) returns the original number, as expressed by the identity a^(log?(x)) = x. This principle is fundamental for simplifying expressions where exponents and logarithms are combined.

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