What is the principal square root of -2500?

Real solutions: none

Complex principal solution: 50i

Step-by-step explanation:

sqrt (-2500)

If we are working with only real numbers, then there is no solution since it is a negative number and negative numbers have to square root in the real domain

If we are in the complex realm

sqrt(-2500) = sqrt(-1) sqrt(2500)

                   = i (50)

We only took the positive values since we are taking the principal square root

                 = 50i

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752

answer: what are the answer choices?

step-by-step explanation: