SOLUTION: Given f(x) = ln x evaluate f(e^(ln3)) f(e^(2ln3))

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Question 926337: Given f(x) = ln x evaluate
f(e^(ln3))
f(e^(2ln3))
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Given f%28x%29+=+ln+%28x%29 evaluate
f%28e%5E%28ln%283%29%29%29=ln%28e%5E%28ln%283%29%29%29 ....ln%283%29=1.098612288668

f%28e%5E%28ln%283%29%29%29=ln%28e%5E%281.098612288668%29%29
f%28e%5E%28ln%283%29%29%29=ln%28e%5E3%29 .............y=ln%28x%29, exponential form is x=e%5Ey
so, e%5E3=e%5Ey => y=3 and
f%28e%5E%28ln%283%29%29%29=3


f%28e%5E%282ln%283%29%29%29=ln%28e%5E%282ln%283%29%29%29
f%28e%5E%282ln%283%29%29%29=ln%28e%5E%28ln%283%5E2%29%29%29
f%28e%5E%282ln%283%29%29%29=ln%28e%5E%28ln%289%29%29%29
f%28e%5E%282ln%283%29%29%29=ln%28e%5E9%29...use same procedure as above:
e%5E9=e%5Ey => y=9
f%28e%5E%282ln%283%29%29%29=9