Question

Find the value of x to make the following equation true.(3^2)^3 x 3^x = (3^7x3^3)/3^11Ax = 1Bx=-7сX = 8DX = -6

Answer 1

Given the expression:

`(3^2)^3\cdot3^x=(3^7\cdot3^3)/(3^(11))`

notice that on the left side, if we simplify, we have the following:

`(3^2)^3\cdot3^x=3^6\cdot3^x=3^(x+6)`

and on the right side, we have:

`(3^7\cdot3^3)/(3^(11))=(3^(7+3))/(3^(11))=(3^(10))/(3^(11))=3^(10-11)=3^(-1)`

then, if we equate both expression we have that:

`3^(x+6)=3^(-1)`

then, this must mean that the exponents are equal. This means the following:

`x+6=-1`

solving for x we get:

`\begin{gathered} x+6=-1 \\ \Rightarrow x=-1-6=-7 \\ x=-7 \end{gathered}`

therefore, x = -7