Problem 41 - Introductory and Intermediate Algebra for College Students 4th

Question

Evaluate each expression without using a calculator. $$8^{\log _{8} 19}$$

Step-by-Step Solution

Answer

The simplified version of the expression \(8^{\log _{8} 19}\) is '19'.

Step 1: Understand the expression

The initial expression is \(8^{\log _{8} 19}\). Here, it's important to understand that the base 8 exponentiation and the base 8 logarithm are inverse operations, so they will cancel each other out.

Step 2: Apply logarithmic rules

Applying the rule \(b^{\log_{b} (n)} = n\), we can simplify \(8^{\log _{8} 19}\) down to just '19'.