Question

Evaluate:  \(\rm log_{0.5}[log_4{(log_2(log_5625))}] = ?\) 
1. 1
2. 0.5
3. 2
4. 4

Answer 1

Correct Answer - Option 1 : 1

Concept:

• \( \rm log_aa=1\)

Calculation:

Given that, \(\rm log_{0.5}[log_4{(log_2(log_5625))}]\)

⇒  \(\rm log_{0.5}[log_4{(log_2(log_55^4))}]\)

⇒  \(\rm log_{0.5}[log_4{(log_2(4log_55))}]\)

⇒  \(\rm log_{0.5}[log_4{(log_2(4))}]\)

⇒  \(\rm log_{0.5}[log_4{(log_22^2)}]\)

⇒  \(\rm log_{0.5}[log_4{(2log_22)}]\)

⇒  \(\rm log_{0.5}[log_4{2}]\)

⇒  \(\rm log_{0.5}[log_4{4^{0.5}}]\)

⇒  \(\rm log_{0.5}[0.5log_4{4}]\)

⇒  \(\rm log_{0.5}[0.5] = 1\)

Hence, option A is correct.