Given that ln 5= 1.099, calculate ln(1/25) to two decimal places.?

Question

Could you please include your steps so I can learn how to do the problem.
Thanx

Answer 1

Two rules to use: ln(a/b) = ln(a) - ln(b), and ln(x^a) = a*ln(x).

So we break up your problem first into ln(1) - ln(25). ln(1) = 0, so we're left with -ln(25). Now 25 = 5^2. So -ln(25) = -ln(5^2) = -2*ln(5).

Then just use what you were given.

Answer 2

The above answers are all correct given that ln 5 = 1.099. However, in reality, ln 5 ≈ 1.609, not 1.099. This is the reason why they don't agree with what you're getting on your calculator (at least I assume that's why you're giving them all thumbs down).

Answer 3

ln (1/25) = ln 5^-2 = - 2 ln 5 = 2(1.099) = -2.198 = ~-2.20

that's it! :)

Answer 4

In general, ln(x^y) = y*ln(x)

ln(5) = 1.609437912 not 1.099

ln(5^-2) = -2*ln(5) = -2.198

Answer 5

ln[1/25]=-2ln5=-2*1.099=-2.198=-2.20approx.

Answer 6

ln(1/25)=ln5^-2=-2ln5=-2(1.099)=-2.20