Question

Example 7: Find x, if X√X=(X√X)^X​

Answer 1

Answer:

hope you understand

Step-by-step explanation:

Take x th root(where x not equal to 0) so powers will divide by x.

Then eq will look like

x^√x =x√x

x^√x = x^(3/2)

x^{√x -(3/2)}=1

Take log in both side

{√x -(3/2)}ln(x) = 0

so x can be 9/4 or 1 .(we can check it by putting these value in original eq

X^(x√x)=(x√x)^x)

In starting of solution we have assumed that

x is not equal to 0. (means answer x is not equal to 0). But what if x=0.

Let's check this case by putting (x=0) in original equation X^(x√x)=(x√x)^x

So we can get 0^0 in both side and 0^0 is not defined. So we can't declare that both sides are equal. So this case is not a solution of x . so x is not equal to 0 .

So x can only be 1 or 9/4 .