Natural Logs (aka Ln)
Important Formulas
*1) ln(xy) = ln(x) + ln (y)
*2) ln(1/x) = -ln(x)
*3) ln(x/y) = ln(x) – ln(y)
*4) ln(x^b) = b * ln(x)
Notation Note
I shall refer to these above formula like so: “*1 means the first formula, which is labeled “*1”
Okay?
The purpose of all of these formulas are to aid in simplification of complicated looking ln functions,
which will in turn help with working with them.
Some Problems
Simplify the following Expressions:
A) ln (5) + ln (x)
Using formula *1 this can become:
ln (5 * x)
B) ln (x^5) – ln (x^3)
First, using formula *3 we get:
ln((x^5)/(x^3))
Using exponential rules:
When the bases (x) are the same, we subtract the powers (5-3)
ln(x^2)
Finally, we use formula *4
2 * ln(x)