Question

if f(x) = 2x - x ln x

show that f(e^3) = -e^3
I know you have to substitute e^3 into the function, so Ive sone ths so far:

2e^3 - e^3 ln e^3
What is the next step?

Answer 1

2e^3 - e^3*lne^3,
lne^3 in exponential form:
e^a = e^3,
Since the 2 sides and bases are equal,
the exponents are also equal.
Therefore,
a = 3. lne^3 = 3.
Substitute e^3 3 for lne^3:

2e^3 - e^3 * 3,
Rearrange 2nd term:
2e^3 - 3e^3 = -e^3.

REMEMBER:
lne = 1,
lne^2 = 2,
lne^3 = 3,
lne^4 = 4.

Answer 2

CORRECTION:
Substitute 3 for lne^3.