Question

There is a problem with this equation in solving equations in Qhere it is if 1/5x=2

Answer 1

Q is the set of the rational numbers

Rational numbers are all numbers that can be put in the form of a/, where b is not equal to zero.

Examples:

`(3)/(4),5(2)/(7),5.4,2`

The given equation is

`((1)/(5))^x=2`

Insert log on both sides

`log\mleft((1)/(5)\mright)^x=log\mleft(2\mright)`

Use the rule of power with a log

`xlog((1)/(5))=log\mleft(2\mright)`

Divide both sides by log(1/5)

`\begin{gathered} x=(log\mleft(2\mright))/(log\mleft((1)/(5)\mright)) \\ x=-0.43067655 \end{gathered}`

Since we can not put the value of x in the form of a/b, then

The equation has NO solution in Q (or empty set { } or Nul)