log3 log4 256x 4SolutionApplying log rule a logbba we get

Solution

Applying log rule : a = log_b(b^a)

we get 4 = log₃(3⁴)

Hence : log₃(log₄(256x) = 4 can be written as log₃(log₄(256x) = log₃(3⁴)

As the logs have same base on both sides , the functions will be equal.

Hence we get (log₄(256x) = 3⁴ = 81

Using a = log_b(b^a) we get 81 = log₄(4⁸¹)

As logs have same bases on both sides , the functions wll be equal.

Hence we get (log₄(256x) = log₄(4⁸¹)

Hence (256x) = (4⁸¹)

Hence (2⁸) x = 2¹⁶²

Hence x = 2^{(162 - 8)} = 2¹⁵⁴

Hence x = 2¹⁵⁴