Question

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.

Answer 1

`\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