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

Question
Logarithms
asked 2021-01-15
Solve the equation and find the exact solution:
\(\displaystyle{\log{{b}}}{a}{s}{e}{2}{\left({\log{{b}}}{a}{s}{e}{3}{\left({\log{{b}}}{a}{s}{e}{4}{\left({x}\right)}\right)}\right)}={0}\)

Answers (1)

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 \(\displaystyle{x}={4}^{{3}}={64}.\)
0

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