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

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