Evaluate the logarithm to the nearest hundredth. In(-100)

Question

A) 10

B) -10

C) Undefined

D) All real numbers

Answer 1

C) Undefined

the domain for logs is x>0

there is no real number for the ln or log of a negative number

Graph y=lnx and all points on the curve are in quadrant I and IV, where x>0, never x<0

log(+100) = 2

log to the base 10 of 100 = 2, 10^2 = 100

which might explain why they tried to entice you to answer A or B

but there is another solution, an imaginary solution

using Euler's Identity

e^ipi = -1 multiply by 100

100e^ipi = -100, take natural logs of both sides to get

ipi + ln100 = ln(-100)

ln(-100) = about 4.6 + ipi or 4.6+3.1i

D) would be correct had it said "no real numbers"

C) is clearly the best answer