Natural log question?

Question

If ln a= 12 and ln b= 4, then what is ln √b ? (that is the square root of b)

Answer 1

ln b = 4

(halve both sides)

½ ln b = 2

(now as n*ln p = ln p^n )

ln b^½ = 2

(Since b^½ = √b)

ln √b = 2

Answer 2

1/2 ln b = 2

Answer 3

ln(b) = ln(√b* √b) = ln(√b) + ln(√b)

If ln(b) = 4 then ln(√b) = 2

Answer 4

ln (b^0.5) = 0.5 ln(b) = 0.5 x 4 = 2

Answer 5

the square root of (e raised to the 4th)

because if you raise both sides of ln b=4 to e then

b=e^4