Log[10log(5log100)]

log[10 log(5 log 100)]
Taking base 10,
log₁₀[10 log₁₀(5 log₁₀100)]
=>log₁₀[10 log₁₀(5*2)]
=>log₁₀[10 log₁₀(10)]
=>log₁₀[10*1]
=>log₁₀(10)
=>1