Question

How do you simplify `ln((5e^x)-(10e^2x))`?

Answer 1

If you meant `ln((5e^x)-(10e^(2x)))`

Then you can factor the `e^x` and use `ln(a*b)=lna+lnb`

`x+ln5+ln(1-2e^x)`

Explanation:

It can't actually. You can't simplify polynomials with exponential functions. The fact that it is substraction (and not multiplication or division) leaves no room for simplifications.

However, if you meant `ln((5e^x)-(10e^(2x)))`

`ln(5e^x-10e^x*e^x)`

Factor the `5e^x`:

`ln(5*e^x*(1-2e^x))`

Use of the property `ln(a*b*c)=lna+lnb+lnc` gives:

`ln5+lne^x+ln(1-2e^x)`

Since `ln=log_e`

`ln5+x+ln(1-2e^x)`