Answer : Option C
Explanation :
Here logb x = ͞5.1342618 is given and log10(x(1/4)) is asked
That means here b also treat as base 10
Now, we can say log10 x = ͞5.1342618 = -5 + 0.1342618 => -4.8657382
Therefore, log10 (x1/4) = ¼ log10 x
Or, ¼ (-4.8657382) = -1.21643455, but it is not in the option.
To make it -2, we have to subtract 0.7835655 from -1.21643455
i.e., -1.21643455 - 0.7835655 = -2
Now, to get back on the original value we have to add 0.7835655 in -2.
Or, -2 + 0.7835655 = ͞2.7835655
Hence, the c is correct.