Let f(x) = log 2 log 3 log 4 log 5 (sinx + a 2 ). Find the set of values of a for which domain of f(x) is R.
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a ∈ 
Sol. Given f(x) = log 2 log 3 log 4 log 5 (sinx + a 2 )
f(x) is defined only if log 3 log 4 log 5 (sinx + a 2 ) > 0, 
x ∈ R
⇒ log 4 log 5 (sinx + a 2 ) > 1, 
x ∈ R ⇒ log 5 (sinx + a 2 ) > 4, 
x ∈ R
⇒ (sinx + a 2 ) > 5 4 , 
x ∈ R ⇒ a 2 > 625 – sinx, 
x ∈ R
⇒ a 2 must be greater than maximum value of 625 – sinx which is 626 (when sinx = –1)
⇒ a 2 > 626 ⇒ a ∈ 
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