Question

Solve each equation.32x – 1 = 16x + 4 2421–2111

Answer 1

Given expression is,

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

let us simplify,

`\begin{gathered} \log (32^(x-1))=\log (16^(x+4)) \\ (x-1)(\log (32))=(x+4)(\log (16)) \\ x-1=(\log(16))/(\log(32))\cdot x+4 \\ x-1=0.8\cdot(x+4) \\ x-1=0.8x+3.2 \\ x-0.8x=3.2+1 \\ 0.2x=4.2 \\ x=(4.2)/(0.2) \\ x=21 \end{gathered}`

The answer is 21.