Question

Solve each equation.32x – 1 = 16x + 4 1) 242) 213) -214) 11

Answer 1

Given the equation;

`32^(x-1)=16^(x+4)`

We express 32 and 16 as an index of 2, we have;

`(2^5)^(x-1)=(2^4)^(x+4)^{}`

Then, we multiply the exponents, we have;

`2^(5x-5)=2^(4x+16)`

So, we take out the 2 from both sides, we have;

`\begin{gathered} 5x-5=4x+16 \\ \end{gathered}`

Then, we collect like terms, we have;

`\begin{gathered} 5x-4x=16+5 \\ x=21 \end{gathered}`

CORRECT OPTION: 21