Question

Evaluate the expression. $\log _{36}(216)$

   Evaluate the expression.
 $\log _{36}(216)$

Precalculus

Carl Stitz, Jeff… 3rd Edition

Chapter 6, Problem 21

Instant Answer

Solved by Expert Nick Johnson

08/14/2021

Step 1

Step 1: We are given the expression $\log _{36}(216)$, which means we are looking for a power that we can raise 36 to get 216. Show more…

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Evaluate the expression. $\log _{36}(216)$

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Key Concepts

Logarithm

A logarithm is the inverse operation of exponentiation. It answers the question: 'to what power must the base be raised to produce a given number?' This concept is fundamental in algebra and calculus for solving equations where the variable is an exponent.

Conversion between Exponential and Logarithmic Forms

One key strategy in evaluating logarithmic expressions is to convert them from logarithmic form to exponential form. This conversion makes it clear that if log_b(a) = c, then b raised to the power c equals a (b^c = a), thereby simplifying the problem-solving process.

Exponent Rules

Exponent rules allow us to rewrite numbers as powers of a common base, which is important when simplifying expressions involving exponents and logarithms. These rules, such as expressing a product or quotient of powers and handling powers raised to another power, are crucial for evaluating logarithms by matching bases and comparing exponents.

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