Question

Hey can u solve using exponential equations? a tutored helped me out but solved it a different way

Answer 1

To find the value of x we need to use the laws of exponents,

First, we use

$\begin{gathered} {(\frac{x}{y})}^a=\frac{{x}^{a}}{{y}^{a}} \\ \frac{1^{x-3}}{36^{x-3}}=216^{2x+2}^{} \\ \frac{1^{}}{36^{x-3}}=216^{2x+2} \end{gathered}$

Then, we we take the numbers to the same base

$\begin{gathered} 36^{-(x-3)}=216^{(2x+2)} \\ (6^2)^{-(x-3)}=(6^3)^{(2x+2)} \\ 6^{-2(x-3)}=6^{3(2x+2)} \end{gathered}$

as we have the same base on both sides, we can cancel them

So, then we have

$\begin{gathered} -2(x-3)=3(2x+2) \\ -2x+6=6x+6 \\ 8x=0 \\ x=0 \end{gathered}$

Finally, the soltion for the equation is x = 0.