The satisfying values of x for the equation 1 divided by X p q equals to one by X 1 by P 1 by q?

Question

The satisfying values of x for the equation 1 divided by X   p   q equals to one by X   1 by P   1 by q?

Answer

Satisfying values of x for the equation 1/X^p*q = 1/X * 1/P * 1/q

Introduction

The given equation is 1/X^p*q = 1/X * 1/P * 1/q. In this equation, we need to find the values of x which satisfy the equation.

Solution

To solve the equation, we can simplify both the sides of the equation.

LHS:

1/X^p*q = (1/X)^(p*q) = (X^(-1))^(p*q) = X^(-p*q)

RHS:

1/X * 1/P * 1/q = (1/X) * (1/P) * (1/q) = (X^(-1)) * (P^(-1)) * (q^(-1)) = (X*P*q)^(-1)

Now, we can equate both the sides of the equation.

X^(-p*q) = (X*P*q)^(-1)

Taking the reciprocal of both sides, we get

X^(p*q) = X*P*q

Dividing both sides by X, we get

X^(p*q - 1) = P*q

Taking the logarithm of both sides, we get

(p*q - 1) log(X) = log(P*q)

Simplifying, we get

log(X) = log(P*q) / (p*q - 1)

Taking the antilogarithm of both sides, we get

X = (P*q)^(1 / (p*q - 1))

This is the value of x that satisfies the equation.

Conclusion

The value of x that satisfies the equation 1/X^p*q = 1/X * 1/P * 1/q is given by X = (P*q)^(1 / (p*q - 1)).

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