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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 G2x13x8 Then X Equals class=

Sagot :

The exponential equation is given to be:

[tex]9^{2x-1}=3^{-x+8}[/tex]

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

[tex]9=3^2[/tex]

Therefore, we have the equation become:

[tex]3^{2(2x-1)}=3^{-x+8}[/tex]

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

[tex]\begin{gathered} 2(2x-1)=-x+8 \\ 4x-2=-x+8 \\ 4x+x=8+2 \\ 5x=10 \\ x=\frac{10}{5} \\ x=2 \end{gathered}[/tex]

The correct answer is OPTION D.

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