The value of the logarithmic function ${log}_{2} {log}_{2} {log}_{2} 16$ is equal to

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Solution

The correct option is D $1$
Using, ${log}_{a} x^{y} = y {log}_{a} x$ and ${log}_{a} a = 1$
${log}_{2} {log}_{2} {log}_{2} 16 = {log}_{2} {log}_{2} {log}_{2} 2^{4} = {log}_{2} {log}_{2} 4 = {log}_{2} {log}_{2} 2^{2} = {log}_{2} 2 = 1$

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