Question

What is the solution to this equation? (1/4) ^x+1 =32 a: 3/2b: 2c: -2d: -7/2

Answer 1

Given

`((1)/(4))^(x+1)=32`

Notice that

`\begin{gathered} 32=2^5 \\ and \\ ((1)/(4))^(x+1)=(1)/(4^(x+1))=4^(-(x+1))=4^(-x-1)=2^(-2x-2) \end{gathered}`

Therefore, the original equation is equivalent to

`\Rightarrow2^(-2x-2)=2^5`

Solving for x,

`\begin{gathered} \Rightarrow-2x-2=5 \\ \Rightarrow x=-(7)/(2) \end{gathered}`

Therefore, the answer is -7/2, option D.