$l o g_{2} 2^{a^{3} - b^{3}}$ =61 (where a and b are consecutive natural numbers and a greater than b ) , then the value of a is

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Solution

The correct option is C
5

$l o g_{2} 2^{a^{3} - b^{3}}$ = $a^{3} - b^{3}$ If a and b are consecutive natural numbers then $a^{3} - b^{3}$ = 1+3ab

61 = 1 + 3 $\times$ 4 $\times$ 5

So, a = 5

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