Question

How to find x- do i have to use logarithms because we just learned them and I do not really get it

Answer 1

The given equation is:

`3^(x+1)=(1)/(81)`

Express the fraction on the right-hand side as a number raised to a power:

`\begin{gathered} 3^(x+1)=(1)/(3^4) \\ \Rightarrow3^(x+1)=3^(-4) \end{gathered}`

Since both expressions have the same base 3, equate the exponents:

`x+1=-4`

Next, solve for x in the equation:

`\begin{gathered} \text{Subtract 1 from both sides of the equation:} \\ x+1-1=-4-1 \\ \Rightarrow x=-5 \end{gathered}`

The value of x is -5.