Sure, let's write the given exponential equation [tex]\(\left(\frac{1}{3}\right)^{-4}=81\)[/tex] in logarithmic form.
The general logarithmic form of an exponential equation [tex]\(a^b = c\)[/tex] is:
[tex]\[
\log_a(c) = b
\][/tex]
Here, the base [tex]\(a\)[/tex] is [tex]\(\frac{1}{3}\)[/tex], the exponent [tex]\(b\)[/tex] is [tex]\(-4\)[/tex], and the result [tex]\(c\)[/tex] is [tex]\(81\)[/tex].
Thus, we can write the given equation [tex]\(\left(\frac{1}{3}\right)^{-4} = 81\)[/tex] in logarithmic form as:
[tex]\[
\log_{\frac{1}{3}}(81) = -4
\][/tex]
So, the logarithmic form of the given equation is:
[tex]\[
\log_{\frac{1}{3}}(81) = -4
\][/tex]
