Algorithms, mathematics, how is such an equation solved?

Question

Mathematics

I started reading the book "Algorithms construction and analysis", at the end of each section there are tasks and no solutions.
Remind me what is the approach in mathematics to solving equations like this:
x ⁸ \u003d 10 ^x
or
8 lg (x) \u003d x

Answer 1

Via the Lambert W-function .

Answer 2

When transferring the right side to the left side, we get a monotone function, and they have exactly one root (if they have at all, check with the Bolzano-Cauchy theorem). Further, approximate methods can be used to obtain a numerical solution or apply methods like the function described above.