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

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

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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.

User Son Lam
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