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- Homework Statement
- If ##\quad\boldsymbol{\displaystyle x^{\displaystyle 2x^{\displaystyle 6}}=3}##, evaluate ##\quad\boldsymbol{\left(x^{\displaystyle x^{\displaystyle x^{\displaystyle 6}}}\right)^{\displaystyle\sqrt 3} = ?}##

- Relevant Equations
- 1. ##a^m \cdot a^n = a^{m\cdot n}##

2. ##\left(a^m\right)^n = a^{mn}##.

3. If ##a^x=b\Rightarrow x\log a=\log b\quad \text{to any base}##

(I can't think of anything else given the little I was able to do in my way of an ##\text{attempt}##.)

**Problem statement : If ##\boldsymbol{\displaystyle x^{\displaystyle 2x^{\displaystyle 6}}=3}##, evaluate ##\boldsymbol{\left(x^{\displaystyle x^{\displaystyle x^{\displaystyle 6}}}\right)^{\displaystyle\sqrt 3} = ?}##**.

**Attempt :**I copy and paste my attempt using Autodesk Sketchbook##^{\circledR}##. I hope I am not violating anything.

**Doubt :**If only I could evaluate ##x##, or so it would seem. Note I have an irrational power ##^{\sqrt 3}## to negotiate with as well.

**A help or a hint would be welcome.**