Respuesta :
Answer:
[tex]x=\frac{-3}{2}[/tex]
Explanation:
We have been given with the expression [tex](1/3)^x=(27)^x+2[/tex]
Now, to solve the equation firstly we have to make the base same on both sides
[tex](1/3)^x=3^{-x}[/tex]
27 can be written as [tex]3^3[/tex]
[tex]27^x=(3^3)^x=3^{3x}[/tex]
Hence, given expression can be rewritten as
[tex]3^{-x}=3^{3(x+2)}[/tex]
Now since, base is same we can equate the powers on both sides
[tex]-x=3(x+2)\\ \Rightarrow-x= 3x+6\\ \Rightarrow -x-3x=6\\-4x=6[/tex][tex]\Rightarrow x=\frac{-3}{2}[/tex]
Therefore given expression [tex](1/3)^x=(27)^x+2[/tex] is equivalent to [tex]x=\frac{-3}{2}[/tex]
Equivalent means the simplified form of any given expression
To find the equivalent expression, we need to expand the given expression by using law of indices.
The equation [tex]3^{-x} = 3^{3x} + 2[/tex] is equivalent to [tex]\left (\dfrac {1}{3}\right )^x = 27 ^x + 2[/tex].
Given:
The given equation is [tex]\left (\dfrac {1}{3}\right )^x = 27 ^x + 2[/tex].
Solving left hand side of the equation.
[tex]\left (\dfrac {1}{3}\right )^x[/tex]
Apply the law of indices.
[tex]\left (\dfrac {1}{3}\right )^x=(-3)^x[/tex]
Solving right hand side of the equation.
[tex]27 ^x + 2=(3^{3x}+2)[/tex]
Thus, the equation [tex]3^{-x} = 3^{3x} + 2[/tex] is equivalent to [tex]\left (\dfrac {1}{3}\right )^x = 27 ^x + 2[/tex].
Learn more about law of indices here:
https://brainly.com/question/13794351
