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