# Indices Question & Equation [closed]

Following is the equation

$$x^{x\sqrt x}=x\sqrt{x}$$

We need to find $$x$$. Please help.

## closed as off-topic by Morgan Rodgers, José Carlos Santos, Paul Frost, Shailesh, YuiTo ChengMay 18 at 2:25

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Morgan Rodgers, José Carlos Santos, Paul Frost, Shailesh, YuiTo Cheng
If this question can be reworded to fit the rules in the help center, please edit the question.

• We have $$x^{x^{1+1/2}}=x^{3/2}$$ – lab bhattacharjee May 17 at 18:28
• $$x=1$$ is one solution. – Dr. Sonnhard Graubner May 17 at 18:30
• $x=0$ is, amazingly, not a solution. – The Count May 18 at 0:17
• Welcome to Mathematics Stack Exchange! A quick tour will enhance your experience. Here are helpful tips to write a good question and write a good answer. – dantopa May 18 at 1:35

HINT

Take logs to get $$x\sqrt{x} \ln x = \ln x + \frac12 \ln x \\ \ln x \left(x \sqrt{x} - \frac32\right) = 0$$

Can you finish?

• @user541396 usually one thinks of $0^0$ as undefined – gt6989b May 19 at 5:19

What if $$x=0$$?

For finite non-zero $$x,$$

$$x^{x^{3/2}-3/2}=1$$

From Find all real numbers $x$ for which $\frac{8^x+27^x}{12^x+18^x}=\frac76$, check if $$u^m=1$$