I have this exercise:
Solve for $x$, $(\log x)^{10} = 3$
My development was:
$\log x = \sqrt[10]3$
$10^{\sqrt[10]3} = x$ , this is my solution.
But I still need a solution, according to the symbolab. Which is: $x = \frac{1}{10^{3^{\frac{1}{10}}}}$
But I have not managed to get it on my own, how can I get to this result? Thanks in advance.
Let's try this with a much simpler problem: suppose you want to find $y$ such that $y^{10} = 1.$
Obviously $y = \sqrt[10]1 = 1$ is a solution.
Is there any other solution? Why or why not?
Your solution method has much in common with the method for finding that $y = 1$ in the example above: you have something to the $10$th power, so you assume all you have to do is take the $10$th root. But this does not give complete solutions, just as taking the square root does not completely solve equations like $x^2 = 1.$