How do you solve log(base 3)(12*log(base 16)x=2

log(base 3)(12*log(base 16)x=2

log₃ (12*log₁₆ (x) )  = 2      this can be written as .......

3^2  = 12*log₁₆ (x)     

9 = 12* log₁₆ (x )    divide both sides by 12

3/4  = log₁₆  (x)      and we can write

16^(3/4)  = x

[16^(1/4) ]^3  = x

2^3  = x

8 = x

Solve for x:

(log((12 log(x))/(log(16))))/(log(3)) = 2

Multiply both sides by log(3):

log((12 log(x))/(log(16))) = 2 log(3)

2 log(3) = log(3^2) = log(9):

log((12 log(x))/(log(16))) = log(9)

Cancel logarithms by taking exp of both sides:

(12 log(x))/(log(16)) = 9

Divide both sides by 12/(log(16)):

log(x) = (3 log(16))/4

(3 log(16))/4 = log(16^(3/4)) = log(8):

log(x) = log(8)

Cancel logarithms by taking exp of both sides:

Answer: |x = 8