Answer :

Certainly! Let's find the exact value of the expression [tex]\( 8^{\log_8 5} \)[/tex] by using properties of logarithms.

1. Understanding the expression:

The expression [tex]\( 8^{\log_8 5} \)[/tex] consists of a base, which is 8, raised to a logarithm with the same base, [tex]\( \log_8 5 \)[/tex].

2. Applying the property of logarithms:

There is a fundamental property of logarithms that states [tex]\( a^{\log_a b} = b \)[/tex]. This means that if you have a number [tex]\( a \)[/tex] raised to the power of the logarithm of another number [tex]\( b \)[/tex] with the same base [tex]\( a \)[/tex], the result simplifies directly to [tex]\( b \)[/tex].

3. Using the property:

In our expression, [tex]\( a = 8 \)[/tex] and [tex]\( b = 5 \)[/tex]. Therefore, we can apply the property as follows:
[tex]\[ 8^{\log_8 5} = 5 \][/tex]

Thus, the exact value of the expression [tex]\( 8^{\log_8 5} \)[/tex] is [tex]\( 5 \)[/tex].