Properties of Logarithms

[nycmathguy]

 

[MathLover1]

f(x)=ln(1-1/x^2)


f(2)+f(3)+f(4)=ln(5/8)

f(2)=ln(1-1/2^2)=ln(1-1/4)=ln(3/4)
f(3)=ln(1-1/3^2)=ln(1-1/9)=ln(8/9)
f(4)=ln(1-1/4^2)=ln(1-1/16)=ln(15/16)

f(2)+f(3)+f(4)=ln(3/4)+ln(8/9)+ln(15/16)

f(2)+f(3)+f(4)=ln((3/4)(8/9)(15/16))
f(2)+f(3)+f(4)=ln((3/4)(8/9)(15/16))...simplify
f(2)+f(3)+f(4)=ln((1/4)(1/1)(5/2))
f(2)+f(3)+f(4)=ln(5/(4*1*2))
f(2)+f(3)+f(4)=ln(5/8) ->proven

 

[nycmathguy]

f(x)=ln(1-1/x^2)


f(2)+f(3)+f(4)=ln(5/8)

f(2)=ln(1-1/2^2)=ln(1-1/4)=ln(3/4)
f(3)=ln(1-1/3^2)=ln(1-1/9)=ln(8/9)
f(4)=ln(1-1/4^2)=ln(1-1/16)=ln(15/16)

f(2)+f(3)+f(4)=ln(3/4)+ln(8/9)+ln(15/16)

f(2)+f(3)+f(4)=ln((3/4)(8/9)(15/16))
f(2)+f(3)+f(4)=ln((3/4)(8/9)(15/16))...simplify
f(2)+f(3)+f(4)=ln((1/4)(1/1)(5/2))
f(2)+f(3)+f(4)=ln(5/(4*1*2))
f(2)+f(3)+f(4)=ln(5/8) ->proven

Nice work like always.