ln 5 = log 5/ln e

ln(x^2-1) - ln (x^3) = ln [(x+1)(x-1)]- 3ln x=ln(x+1)+ln(x-1)-3*ln x2. write "ln(x^2-1)/x^3)" as a sum, difference and/or constant multiples of logarithms. I got "ln(x^2-1)-3lnx" for this.

9/300=3003. Simplify "log(9/300)". I got "log3"

Thus,

log 9/300 = log 300 = log 3*10^2 = log 3 + log 10^2=log 3+2

Note4. Simplify -8+e^(ln(x^3)). I have no idea how to solve this one

e^(ln x)=x for all positive x.

Now,

ln x^3 = 3ln x

Thus,

e^(ln(x^3))=e^(3ln x)=(e^(ln x))^3 (by the exponent laws).

But then,

(e^ln(x))^3=x^3.

Or, an easier way.

Let y=x^3.

Thus,

e^(ln y) = y= x^3.

This is Mine 5-th Post!!!