How to solve (16^(log4 x))=4

My results is not correct.

16^(log₄x) = 4
(2^4)^(log₄x) = 2^2
2^(4 log₄x) = 2^2

4 log₄x = 2
log₄x = 1/2
4^log₄x = 4^(1/2)
x = 2

Note that x = -2 is not a valid answer, since you can't have log of negative number

Ματπmφm

y=logb(x) equivalent to x=b^y

I would take the log of both sides.

so you get
log(16)*log4(x) = log(4)
divide both sides by log(16)
log4(x) = log(4) / log(16)
apply the top equation
x=4^( log(4) / log(16) )
x=2

I could be wrong on this. I hope not.

16^(something) = 4
So the "something" part is = 0.5

log4 x = 0.5
So 4^(0.5) = x, which means that x = +2 or x = -2.

Note: the logarithm of a negative number is probably too advanced for your class.

16 ^ (log4 x) = 4
log4 x = log16 4
log4 x = log16 (16^(1/2))
log4 x = (1/2) * log16 16
log4 x = 1/2
x = 4 ^ (1/2)
x = 2