In a previous course you learned how to solve “power equations” of the form $x^a=b$, where $a$ and $b$ are real numbers, by raising each side to a well-chosen power. Review this method by completing the parts below.  

1. Equation: $x^{1.05}=2$
   Start by estimating the solution so that you know what to expect when you use a calculator.

2. Algebraically solve the equation. Write your answer in exact form.

   Step (b):

   $\left(x^{1.05}\right)^{1/1.05}=2^{1/1.05}$

3. Use a calculator to obtain a value for $x$ accurate to three decimal places.

4. Explain why logarithms are not needed to solve the equation.