Sure, let's rewrite each equation as requested, step by step.
### Part (a) Rewrite as an exponential equation
Given the logarithmic equation:
[tex]\[
\log_8 1 = 0
\][/tex]
We need to convert this to an exponential equation. Recall the definition of a logarithm: [tex]\(\log_b a = c\)[/tex] is equivalent to [tex]\(b^c = a\)[/tex].
In this case:
[tex]\[
\log_8 1 = 0
\][/tex]
Using the logarithm definition:
[tex]\[
8^0 = 1
\][/tex]
So, the exponential form of [tex]\(\log_8 1 = 0\)[/tex] is:
[tex]\[
8^0 = 1
\][/tex]
### Part (b) Rewrite as a logarithmic equation
Given the exponential equation:
[tex]\[
3^4 = 81
\][/tex]
We need to convert this to a logarithmic equation. Recall that [tex]\(b^c = a\)[/tex] is equivalent to [tex]\(\log_b a = c\)[/tex].
In this case:
[tex]\[
3^4 = 81
\][/tex]
Using the exponential to logarithm conversion rule:
[tex]\[
\log_3 81 = 4
\][/tex]
So, the logarithmic form of [tex]\(3^4 = 81\)[/tex] is:
[tex]\[
\log_3 81 = 4
\][/tex]
### Final Answers:
(a) [tex]\(8^0 = 1\)[/tex]
(b) [tex]\(\log_3 81 = 4\)[/tex]
So, filling in:
(a) [tex]\(8^0 = 1\)[/tex]
(b) [tex]\(\log_3 81 = 4\)[/tex]
