Question 1093270
4^(2x) = 16


take the log of both sides to get log(4^(2x)) = log(16)


this is equivalent to 2x * log(4) = log(16)


divide both sides by log(4) to get 2c = log(16)/log(4)


divide both sides by 2 to get x = log(16)/log(4)/2


use your calculator to get x = 1


you could also have done:


4^(2x) = 16


since you know that 4^2 = 16, then you get:


4^(2x) = 16 and 4^2 = 16


since they're both equal to 16 then they're both equal to each other and you get:


4^2 = 4^(2x)


this can only be true if 2 = 2x.


solve for x to get x = 1.


note that the properties of logs and exponents that were used were:


log(x^a) = a*log(x)


if x^a = x^b, then a = b