Question

# Solve the equation and find the exact solution: log base 2( log base 3( log base 4(x)))=0

Logarithms
Solve the equation and find the exact solution:
$$\displaystyle{\log{{b}}}{a}{s}{e}{2}{\left({\log{{b}}}{a}{s}{e}{3}{\left({\log{{b}}}{a}{s}{e}{4}{\left({x}\right)}\right)}\right)}={0}$$

2021-01-16
Start with $$\displaystyle{x}={4}^{{3}}={64},$$
log[4](64)=3,
log[3](3)=1,
log[2](1)=0,
so x=64 is a solution.
Another way: log[2](z)=0,
so z=1, log[3](y)=1,
so y=3, log[4](x)=3,
so $$\displaystyle{x}={4}^{{3}}={64}.$$