Question

Solve the equation: " alt="5^x^(^x^-^1^)=1" align="absmiddle" class="latex-formula">

Answer 1

The concept:

We are given the equation:

$5^{x(x-1)} = 1$

Which can be simplified as:

$5^{x^{2} - x} = 1^{1}$

Since any number to the power '0' is 1

x² - x must be equal to 0 for the given equation to be true

Solving for x:

x² - x = 0

x(x-1) = 0

now, we can divide both sides by either x OR x-1

So we will see what we get for either choice:

x = 0/(x-1)                           x-1 = 0/x

x = 0                                  x = 1

Hence, the value of x is either 0 or 1