Questions: Evaluate the following expression without using a calculator. 3^(log3 8) 3^(log3 8)=

Evaluate the following expression without using a calculator. 3^(log3 8) 3^(log3 8)=
Transcript text: Evaluate the following expression without using a calculator. \[ 3^{\log _{3} 8} \] \[ 3^{\log _{3} 8}= \] $\square$
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Solution

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Solution Steps

Step 1: Understand the Expression

The expression given is \(3^{\log_{3} 8}\). This is an example of an exponential expression where the base of the exponent is the same as the base of the logarithm.

Step 2: Apply the Logarithmic Identity

There is a logarithmic identity that states:

\[ a^{\log_{a} b} = b \]

This identity can be applied directly to the expression \(3^{\log_{3} 8}\).

Step 3: Simplify the Expression

Using the identity from Step 2, we can simplify the expression:

\[ 3^{\log_{3} 8} = 8 \]

Final Answer

\[ \boxed{8} \]

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