Simplify the expression.

Question

1 + ln(e^4x)

Answer:

Answer 1

ln(e^4x) = 4xlne = 4x

the power of e comes out as a coefficient, then the natural log of e = 1 leaving only 4x

so

1+ln(e^4x) = 1+ 4x

Answer 2

1+ ln(e^(x+x+x+x)) =

1+ ln ( e^x * e^x * e^x * e^x)

1+ ln(e^x) + ln(e^x) + ln(e^x) + ln(e^x)

= 1 + x+x+x+x

= 4x+1