Indices and Log Questions
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Solve 2a^(lg 3) x 3^(lg a) - 5a^(lg3) = 3 where a is a constant.
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Tip:
Log both sides, and remember to bring down the power ;)
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Originally posted by Snoopyies:
Solve 2a^(lg 3) x 3^(lg a) - 5a^(lg3) = 3 where a is a constant.
Hi,
one thing which you must understand is that a^(lg3) is the same as 3^(lga).
Thus, you can rewrite the whole equation as 2X3^(lga) X 3^(lga) - 5X3^(lga) = 3.
If we let 3^(lga) be u, we will have 2u^2 - 5u - 3 = 0, which is the same as (2u+1)(u-3)=0
u = -1/2 is rejected in this case, and you should be able to see why.
Thus, u=3, 3^(lga)=3, lga=1, and a=10.
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Originally posted by TrueHeart:
Hi,
one thing which you must understand is that a^(lg3) is the same as 3^(lga).
Thus, you can rewrite the whole equation as 2X3^(lga) X 3^(lga) - 5X3^(lga) = 3.
If we let 3^(lga) be u, we will have 2u^2 - 5u - 3 = 0, which is the same as (2u+1)(u-3)=0
u = -1/2 is rejected in this case, and you should be able to see why.
Thus, u=3, 3^(lga)=3, lga=1, and a=10.
Hi,
How come a^(lg3) is the same as 3^(lga) ?
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Originally posted by Snoopyies:
Hi,
How come a^(lg3) is the same as 3^(lga) ?
Hi,
a^(lgb) = b^(lga) for all a and b > 0.
Proof:
Assuming that the hypothesis a^(lgb) = b^(lga) is true,
a^(lgb)=b^(lga)
lga^(lgb)=lgb^(lga)
(lgb)(lga)=(lga)(lgb)
There you go.
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Another Method
Question
lg b lg a
Prove that a = b
Steps
lg b
(1) LHS = a
(2) Convert into loga
loga b
--------
loga 10
= a
loga b ( 1/ loga 10)
= a
loga b
(3) Using the rule a = b
1
--------
loga 10
= b
(4) Convert into lg
1
--------------
lg 10
------
lg a
= b
lg a
= b
lg b lg a
a = b
Hence, LHS = RHS (Proved)
lg a lg 3
PS : Thus, 3 = a
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wah seh
i learn this last semester and i forgot everything now
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Originally posted by gunner77:
wah seh
i learn this last semester and i forgot everything now
Hi Gunner,
How are your studies in poly ? Must be fine right ?
There must be many exciting activties in poly too right ?
Share them in your forum also lah.
Regards.
PS : Just curious that why are there no poly students come into homework forum to ask questions ?
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Originally posted by Lee012lee:
Hi Gunner,
How are your studies in poly ? Must be fine right ?
There must be many exciting activties in poly too right ?
Share them in your forum also lah.
Regards.
PS : Just curious that why are there no poly students come into homework forum to ask questions ?
Mr Lee, I can clear your curiousness. In poly, it's damn easy to pass. After one semester I realise one thing, In poly, Its not about passing. Its about scoring. Because in poly, if you got come to school and submit your work etc etc, you are already getting a grade D ( D is a pass for poly ). I was told by my friends that unless you never come to school or didn't write anything for exams, you are more or less pass. In poly, as long as you fail, the lecturer have to write a report and explain to the module coordinater why you fail. So some will be very lazy to write the report and make you pass. Poly student know this, thats why they always aim for the grade D.Only those who want to get As will post in this forum.
Btw I get B+ for engineering maths
so happy! but i think i forget everything now and thanks for asking Mr Lee, Im managing well in poly. everything is within my pace. i set my own pace of studying.
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Originally posted by gunner77:
Mr Lee, I can clear your curiousness. In poly, it's damn easy to pass. After one semester I realise one thing, In poly, Its not about passing. Its about scoring. Because in poly, if you got come to school and submit your work etc etc, you are already getting a grade D ( D is a pass for poly ). I was told by my friends that unless you never come to school or didn't write anything for exams, you are more or less pass. In poly, as long as you fail, the lecturer have to write a report and explain to the module coordinater why you fail. So some will be very lazy to write the report and make you pass. Poly student know this, thats why they always aim for the grade D.Only those who want to get As will post in this forum.
Btw I get B+ for engineering maths
so happy! but i think i forget everything now and thanks for asking Mr Lee, Im managing well in poly. everything is within my pace. i set my own pace of studying.
Hi Gunner,
Congratulations for the good results.
Keep up with the good work.
Regards.
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Originally posted by Lee012lee:
Hi Gunner,
Congratulations for the good results.
Keep up with the good work.
Regards.
Eh mr lee, crap more at my forum leh.Dont tell me u only teach but dont talk cock?