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

How to find x- do i have to use logarithms because we just learned them and I do not-example-1
User MEURSAULT
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1 Answer

18 votes
18 votes

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.

User Fran Cerezo
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