Please show all of the steps Solve for x log4 log4 x 3Solut

Please show all of the steps

Solve for x: (log_4 (log_4 x)) = 3

Solution

Solution:

Given that

log₄(log₄ (x)) =3 ...1

Now

3 = log₄ 4³ { Log_{b b}^c = c log_bb = c}

3 = log₄ 64

from (1)

log₄64 = log₄ (log₄(x))

thus it reduces to

log₄ (x) = 64

Now

64 = log₄ 4^{64 .....} { Log_{b b}^c =  c log_bb = c}

log₄(x) =  log₄ 4⁶⁴

this reduces to

x = 4⁶⁴

Answer