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Use the equation below to complete the following problems.a.) Rewrite the equation using the same base.b.) Solve for x. Write your answer in simplest form.

Use the equation below to complete the following problems.a.) Rewrite the equation-example-1

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Solution


\begin{gathered} 8^(2x)=32^(x+3) \\ \\ \text{ since }8=2^3\text{ and }32=2^5 \\ \\ \Rightarrow(2^3)^(2x)=(2^5)^(x+3) \\ \\ \Rightarrow2^(3(2x))=2^(5(x+3))\text{ \lparen Equating the power\rparen} \\ \\ \Rightarrow3(2x)=5(x+3) \\ \\ \Rightarrow6x=5x+13 \\ \\ \Rightarrow6x-5x=13 \\ \\ \Rightarrow x=13 \end{gathered}

Therefore, x = 13

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