Question

Solve an exponential equation by rewriting the base. g^(2x-1)=3^(-x+8), then x equals __________.

Answer 1

The exponential equation is given to be:

`9^(2x-1)=3^(-x+8)`

We can make the base of both sides be equal. We know that:

`9=3^2`

Therefore, we have the equation become:

`3^(2(2x-1))=3^(-x+8)`

Since the bases are equal now, we can equate it and solve as shown below:

`\begin{gathered} 2(2x-1)=-x+8 \\ 4x-2=-x+8 \\ 4x+x=8+2 \\ 5x=10 \\ x=(10)/(5) \\ x=2 \end{gathered}`

The correct answer is OPTION D.