Question

Write in logarithmic form. $$3^{-4}=\frac{1}{81}$$

   Write in logarithmic form.
$$3^{-4}=\frac{1}{81}$$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 2nd Edition

Chapter 13, Problem 21

Instant Answer

Solved by Expert Liuxi Sun

06/25/2020

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Step 1: We are given the equation in exponential form: $3^{-4}=\frac{1}{81}$. Show more…

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Write in logarithmic form. $$3^{-4}=\frac{1}{81}$$

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Key Concepts

Exponential Equations

Exponential equations involve expressions where a number, called the base, is raised to an exponent. This form, represented as a^b = c, lays the groundwork for understanding how logarithms function as the inverse of exponentiation. Recognizing the structure of these equations helps in identifying which part of the equation corresponds to the base, exponent, and result.

Logarithmic Form

Logarithms are the inverse operations of exponentiation. When an exponential equation is given as a^b = c, it can be rewritten in its logarithmic form as b = log_a(c). This conversion is crucial for solving equations where the unknown is an exponent, as it transforms the problem into one that involves calculating logarithms.

Negative Exponents

Negative exponents indicate the reciprocal of a positive exponent. In general, a negative exponent such as a^(-b) means 1/(a^b). This understanding is important when converting exponential expressions into logarithmic form, as it shows how reversing the operation of exponentiation relates to the concept of reciprocals in mathematics.

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