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

1 Answer
Costas C.
Jan 2, 2016

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)#

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