Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b

Determine whether the statement is true or false. If 0 < a < b, then Ln a < Ln b

We have a logarithmic property that states:
ln(a) - ln(b) = ln (a / b)

We're given a < b, so (a / b) < 1

Therefore:

ln (a / b) < 0

And since ln(a) - ln(b) = ln (a / b)

Then Ln(a) - Ln(b) < 0

Add Ln(b) to each side and we get:
Ln(a) - Ln(b) + Ln(b) < 0 + Ln(b)

Cancel the Ln(b) on the left side and we get:
Ln(a)<Ln(b)

So this is TRUE