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:

$\frac{3}{4},5\frac{2}{7},5.4,2$

The given equation is

$(\frac{1}{5})^x=2$

Insert log on both sides

$log\mleft(\frac{1}{5}\mright)^x=log\mleft(2\mright)$

Use the rule of power with a log

$xlog(\frac{1}{5})=log\mleft(2\mright)$

Divide both sides by log(1/5)

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

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)