Prove this? (2 Viewers)

[azureus88]

thats the problem....that argument relies IF the original equality holds

we have to PROVE that it holds, and therefore CANNOT assume that it holds in the first place

However, if the equality doesnt hold, then adding ln0.5 to both sides WONT preserve the equality. I agree with this.

But notice how the guy actually goes on to prove that it does actually preserve the quality (and hence that the original equality is true). He goes this in the step LHS=ln2+ln0.5=ln1=0=RHS

 

[micuzzo]

thats the problem....that argument relies IF the original equality holds

we have to PROVE that it holds, and therefore CANNOT assume that it holds in the first place

u make a good point... but i dont i think i would have changed anything by addin ln0.5 to both sides... its still the same just rearranged (issnt it???)... coz wat happens wiff those types of questions where u have to rearrange both sides first... wouldnt this change the equality

 

[Timothy.Siu]

u make a good point... but i dont i think i would have changed anything by addin ln0.5 to both sides... its still the same just rearranged (issnt it???)

but then thats different. if u wanted to do it like that...i think u'd have to set it out differently.

u'd have to say
Prove ln2+ln 0.5=ln 0.5 - ln 0.5
RHS=ln1=0=LHS

therefore ln2+0.5=ln 0.5-ln 0.5
and hence ln2=-ln 0.5

but doing this would just be working backwards...might not work for harder questions

 

[GUSSSSSSSSSSSSS]

LOL well im now LESS sure.....however i still believe that by adding and subtracting from BOTH sides then that is still relying on ASSUMING that the equality holds

....however then again im not the BEST mathematician in the world so i may be wrong =S

 

[micuzzo]

but then thats different. if u wanted to do it like that...i think u'd have to set it out differently.

u'd have to say
Prove ln2+ln 0.5=ln 0.5 - ln 0.5
RHS=ln1=0=LHS

therefore ln2+0.5=ln 0.5-ln 0.5
and hence ln2=-ln 0.5

but doing this would just be working backwards...might not work for harder questions

hmm... ic wat u mean...

 

[azureus88]

ok, consider this: We have 3 numbers, A, B and C,

then A+C=B+C if and only if A=B

so proving A+C=B+C is the same as proving A=B, no?

 

[Timothy.Siu]

ok, consider this: We have 3 numbers, A, B and C,

then A+C=B+C if and only if A=B

so proving A+C=B+C is the same as proving A=B, no?

not exactly the same, but by proving one u can say the other one is true

 

[GUSSSSSSSSSSSSS]

thats a complete different case....for starters in that example you are not proving that A + C = B + C ...you are proving that A + C = B + C ...if and only if A = B.....=S

 

[micuzzo]

how about:

ln2=-ln0.5

ln2 + ln0.5 = 0

LHS = ln1=0=RHS

Q.E.D

here let me sort this out... i think the proof would still work because for the statement to hold true, LHS can = RHS = 0.

maybe if i had set it out like this:

Prove: ln2 = -ln0.5

Comment / Construction: If the statement holds true, then

ln2 + ln0.5 = 0 ---------- (1)

since lna + lnb = ln(a/b) ,

(1) = ln1

but ln1 = 0 (by calculation)

therefore LHS = RHS = 0

so the statement, ln2 = -ln0.5 must hold true

Q.E.D


but it is easier to just do as Timothy.Siu said.

However i still think my initial proof is correct [that doesnt mean i endorse it lol], it just needed to be set out better.