Solve the equations a Xxx Xxx b pi xlog pi exlog eSolution

Solve the equations: a) X^(x^x) = X^(x^x) b) (pi x)^log pi = (ex)^log e.

Solution

Solution:

A)

x^{(x^x)} = (x^x)^x

Taking log both sides:

(x^x) log x = x log x^x

=> (x^x) log x = x² logx

=> x^(x-2) = 1

=> x^(x-2) = x⁰

=> x - 2 = 0

=> x = 2

B)

Here;

Take log on both sides:

log() (log()+log(x)) = log(e)(log(e)+log(x))

log() log(x) - log(e) log(x) = (log(e))^2 - log())^2

=> log() log(x) - log(e) log(x) = (log(e)+log())(log(e)-log())

=> log(x) = - [log(e)+log()]

=> log(x) = - log(e)

=> x = 1/(e)