The given equation is:
[tex]3^{x+1}=\frac{1}{81}[/tex]
Express the fraction on the right-hand side as a number raised to a power:
[tex]\begin{gathered} 3^{x+1}=\frac{1}{3^4} \\ \Rightarrow3^{x+1}=3^{-4} \end{gathered}[/tex]
Since both expressions have the same base 3, equate the exponents:
[tex]x+1=-4[/tex]
Next, solve for x in the equation:
[tex]\begin{gathered} \text{Subtract 1 from both sides of the equation:} \\ x+1-1=-4-1 \\ \Rightarrow x=-5 \end{gathered}[/tex]
The value of x is -5.
