Question

Evaluate the expression. $$ \log _{3} \sqrt{27} $$

   Evaluate the expression.
$$
\log _{3} \sqrt{27}
$$

Algebra and Trigonometry

Algebra and Trigonometry

James Stewart,… 2nd Edition

Chapter 5, Problem 1

Instant Answer

Solved by Expert Amy Jiang

08/26/2020

Step 1

The square root of a number is the same as raising that number to the power of 1/2. So, we can rewrite the expression as: $$ \log _{3} 27^{1/2} $$ Show more…

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Evaluate the expression. $$ \log _{3} \sqrt{27} $$

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Key Concepts

Properties of Exponents and Logarithms

Key properties, such as the rule that log_b(b^x) = x, allow for the straightforward evaluation of logarithmic expressions once the argument has been expressed as a power of the base. These properties are essential for manipulating and simplifying both logarithmic and exponential expressions in a variety of mathematical contexts.

Logarithms

A logarithm is the inverse operation to exponentiation, indicating the power to which a given base must be raised to obtain a specific number. This concept is fundamental in solving equations where the unknown is an exponent, and it allows for the transformation of multiplicative relationships into additive ones.

Exponents and Radical Expressions

Radical expressions, such as roots, can be rewritten using exponents with fractional values. For example, the square root of a number can be represented as that number raised to the power of 1/2. This conversion is crucial for applying exponent rules to simplify and evaluate expressions involving radicals.

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