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} {((x)/(y))}^a=\frac{{x}^(a)}{{y}^(a)} \\ (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.