If f(x) =ln(1-1/x2). The value of f(2)+f(3)+f(4) is
Answers
Given: The function f(x) = ln(1 - 1/x^2)
To find: The value of f(2)+f(3)+f(4) ?
Solution:
- Now we have given the function f(x) = ln(1 - 1/x^2)
- So:
f(2)+f(3)+f(4) = ln(1 - 1/2^2) + ln(1 - 1/3^2) + ln(1 - 1/4^2)
= ln(1 - 1/4) + ln(1 - 1/9) + ln(1 - 1/16)
= ln(3/4) + ln(8/9) + ln(15/16)
= ln 3 - ln 4 + ln 8 - ln 9 + ln 15 - ln 16
= ln 3 - 2ln 2 + ln (4x2) - 2ln 3 + ln (3x5) - 2ln 4
= ln 3 - 2ln 2 + ln 4 + ln 2 - 2ln 3 + ln 3 + ln 5 - 4ln 2
= ln 3 - 2ln 2 + 2 ln 2 + ln 2 - 2ln 3 + ln 3 + ln 5 - 4ln 2
- Now simplifying this, we get:
= -3 ln 2 + ln 5
= -3(0.693) + 1.609
= -2.079 + 1.609
= 0.47
Answer:
So the value of the given expression is 0.47.
Answer:
Step-by-step explanation:
ln(5/8)
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