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?
2e^3-e^3lne^3=
2e^3-e^3*3=-e^3
34= ln (e^34)
To simplify the expression f(e^3) = 2e^3 - e^3 ln(e^3), follow these steps:
Step 1: Simplify the natural logarithm term.
Since ln(e^3) is the natural logarithm of e^3, which is equal to 3, you can simplify it to 3.
Step 2: Substitute the simplified expression into the original function.
Replace ln(e^3) with 3 in the expression 2e^3 - e^3 ln(e^3):
f(e^3) = 2e^3 - e^3 * 3
Step 3: Simplify the remaining expression.
Multiply e^3 and 3, which gives you 3e^3:
f(e^3) = 2e^3 - 3e^3
Step 4: Combine like terms.
Subtract 3e^3 from 2e^3:
f(e^3) = -e^3
Therefore, f(e^3) simplifies to -e^3.