To write the exponential equation [tex]\(8^5 = 32768\)[/tex] in logarithmic form, we can express this relationship in three different ways:
1. Using the base 8:
Recall that the logarithmic form of [tex]\(a^b = c\)[/tex] is [tex]\(\log_{a} c = b\)[/tex]. In this case, the base is 8, the exponent is 5, and the result is 32768. So, we can write:
[tex]\[
\log_{8} 32768 = 5
\][/tex]
2. Using the exponent as the base:
Alternatively, we can consider the exponent 5 as the base. In that case, the relationship can be written as:
[tex]\[
\log_{5} 32768 = 8
\][/tex]
3. Using the result as the base:
We can also consider the result 32768 as the base. Using the same principle, we write:
[tex]\[
\log_{32768} 8 = 5
\][/tex]
These three forms represent the same exponential equation [tex]\(8^5 = 32768\)[/tex] in logarithmic notation.
