REMEMBER! loge = ln
OK, for this first slide he used 3 logarithmic identities to form the single logarithm
1. ln(x-1) + 3ln(x+3) becoming the numerator(x-1)(x+3)^3 from
the identity log e (MN)= log e M + log e N
2.from (ln(x-1)+3ln(x+3))-1/2ln(x^2+2) he got the denominator Square Root of (x^2+2) which is the same as(x^2+2)^1/2 from the identity log e (M/N) = log e M - log e N
3. and the third identity is log e (M^N) = N log e M which you can see done with both the numerator and denominator
the only thing i think i need to explain with this one is that if both sides of an equation have loge
in front we know we can take it away, correct? so i guess the opposite can be done as well where we add in loge, which is seen done in the second line (the red ink).
(remember! loge = ln)!
*lne=1
this slide uses the third identity mentioned in the first slide, and takes away ln from both sides(as mentioned in slide two), other than that i think it is self explanatory.
in this slide he adds ln to both slides making lne on the left side which previously stated equals one(see lime green * in above slides explination).
and again he used the third identity mentioned in slide 1.
Hope this helped you in anyway, shape, or for possible
Mr. Maksymchuk gave use another one of his shirt ideas this one was based on the Pink Floyd album cover the dark side of the moon with the rainbow and prisms, but his shirt would say Pink Freud. I didn't get the reference but maybe you did.
I later googled it and it was referanced to Sigmund Freud who was a phsycoanalysis who was best know for his theories of the unconcious mind and the defence mechanism of repression.
after all that i still didn't completely get it, oh well, my loss I guess
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