Jibu ni 2, tatizo ni njia

[SMU]

Jibu hili hapa wakuu:

2^x=2x......eqn (1)
Apply log both sides
Log2^x=log2x
log2^x=log2+logx
log2^x-logx=log2
log division rule
Log(2^x/x)=log2
Compare log values
2^x/x=2
2^x=x2......eqn (2)

Substitute value of 2^x in eqn (1)
Therefore:
X2=2x
Divide by x both sides:
X=2.

Duh....kazi ipo! Hiyo eqn(1) na eqn(2) zina tofauti gani?

 

[NingaR]

Jibu hili hapa wakuu:

2^x=2x......eqn (1)
Apply log both sides√
Log2^x=log2x√
log2^x=log2+logx√
log2^x-logx=log2√
log division rule
Log(2^x/x)=log2√
Compare log values
2^x/x=2√
2^x=x2......eqn (2)kwanini hapa umeita …eqn(2) kwani inatofauti na …eqn(1)??

Substitute value of 2^x in eqn (1)X
Therefore:
X2=2xX
Divide by x both sides:
X=2.X

Kijana naona hesabu kwako ni janga kubwa sana!!

 

[Prisoner 46664]

Duh....kazi ipo! Hiyo eqn(1) na eqn(2) zina tofauti gani?

Eqn 1 inalinganisha two power x na two x mkuu...
Wakati eqn 2 inalinganisha two power x na x square..
Kwa ivo automatically two x inakuwa sawa sawa na x square

 

[platozoom]

Mnahangaika sana hilo swali jibu lake unalipata kwenye kitabu cha Chinua Achebe "Things fall apart"

 

[Shakir]

Jibu hili hapa wakuu:

2^x=2x......eqn (1)
Apply log both sides
Log2^x=log2x
log2^x=log2+logx
log2^x-logx=log2
log division rule
Log(2^x/x)=log2
Compare log values
2^x/x=2
2^x=x2......eqn (2)

Substitute value of 2^x in eqn (1)
Therefore:
X2=2x
Divide by x both sides:
X=2.

Unajua ulichofanya??
Ni sawa Na kusema.
2^x =2 x..........(1)

Square both sides
(2^x)^2 = (2x)^2

Then take a root of both sides after being squared
Will return to
(2^x) = 2x .......(2)

IS IT??!!!
Typically forging mkuu.
Then una-compare kati ya (1) na (2) ambazo ni kitu kilekile,
NO bana, can't be!!

 

[Prisoner 46664]

Unajua ulichofanya??
Ni sawa Na kusema.
2^x = x..........(1)

Square both sides
(2^x)^2 = (2x)^2

Then take a root of both sides after being squared
Will return to
(2^x) = 2x .......(2)

IS IT??!!!
Typically forging mkuu.
Then una-compare kati ya (1) na (2) ambazo ni kitu kilekile,
NO bana, can't be!!

Kaka chukua karatasi uandike hatua moja baada ya nyingine..hiyo njia inaleta logic..niambie mathematically nimekosea nini..coz hapo trick ni kutengeneza equation ambazo unaweza kusolve kama quadratic au simple algebra..soma vizuri

 

[Shakir]

Kaka chukua karatasi uandike hatua moja baada ya nyingine..hiyo njia inaleta logic..niambie mathematically nimekosea nini..coz hapo trick ni kutengeneza equation ambazo unaweza kusolve kama quadratic au simple algebra..soma vizuri

tatizo unachukua equation moja unai-manuva na kuleta ingine ziwe mbili ambayo infact haina tofauti na ya kwanza.

Swali lina equation moja tu,
Unaliundia equations mbili tofauti ili ulazimishe lije katika "smultaneously".

 

[ruhi]

Answers might be many including 2,this question should be solve by ploting the graph as shown below:

 

[Preta]

interesting....very....
haya sasa....leteni hesabu nyingine tusolve.....

 

[Prisoner 46664]

Kijana naona hesabu kwako ni janga kubwa sana!!

Kaka sidhani kama umeona kuwa kuna tofauti kubwa sana kati ya eqn 1 na 2...biiiiig difference...angalia vizuri mkuu..

Alafu pia,njia ya kuchora graph ingefaa pia..
Let 2^x=2x=y
Unachora graph 2 za y
Y=2^x....eqn 1
Na graph ya pili
Y=2x...eqn 2

Hizo graph mbili zinapointersect unapata value za y alafu unaweka kwenye equation yeyote kupata x..mchezo kwisha

 

[SMU]

Eqn 1 inalinganisha two power x na two x mkuu...
Wakati eqn 2 inalinganisha two power x na x square..
Kwa ivo automatically two x inakuwa sawa sawa na x square

Yaani ulitaka kusema hivi: 2^x=2x na 2^x=x^2? Sasa tizama vizuri ulichoandika mwanzo. Hata hivyo hiyo x^2 itakuja kivipi katika hiyo eqn yako ya pili?

 

[Prisoner 46664]

tatizo unachukua equation moja unai-manuva na kuleta ingine ziwe mbili ambayo infact haina tofauti na ya kwanza.

Swali lina equation moja tu,
Unaliundia equations mbili tofauti ili ulazimishe lije katika "smultaneously".

Kaka hizi ndo zinaitwa maths tricks sasa..kumanipulate swali ili lije kwenye njia inayoweza kusolvika kwa urahisi..ni ngumu ku-deal na uknown variables zikiwa kwenye exponents thats y..maana bila hiyo trick the only easy way ni kuchora graph tu..which takes a lot of energy

 

[Shakir]

interesting....very....
haya sasa....leteni hesabu nyingine tusolve.....

Penda hii Rangi,
Boga likipendwa, Na Ua pia linahusika.

Btw, kwenye ile thread ya kutaja marital status sijaiangalia yako bado as I promised earlier.

 

[NingaR]

Eqn 1 inalinganisha two power x na two x mkuu...
Wakati eqn 2 inalinganisha two power x na x square..
Kwa ivo automatically two x inakuwa sawa sawa na x square

kijana umedanganya uma!! kwani sikuhizi hesabu ikiwa hivi
(2^x)/x=2 inakua (2^x)=x²
sio inakua (2^x)=2x?? au hesabu imebadilika siku hizi??

 

[Preta]

Penda hii Rangi,
Boga likipendwa, Na Ua pia linahusika.

Btw, kwenye ile thread ya kutaja marital status sijaiangalia yako bado as I promised earlier.

ooh yeah....achana na yale ya kule....mi niko single and fresh.....najua wananzi hawawezi kuja hapa kwenye hesabu.....wewe usiwe na wasiwasi......

 

[Shakir]

Kaka hizi ndo zinaitwa maths tricks sasa..kumanipulate swali ili lije kwenye njia inayoweza kusolvika kwa urahisi..ni ngumu ku-deal na uknown variables zikiwa kwenye exponents thats y..maana bila hiyo trick the only easy way ni kuchora graph tu..which takes a lot of energy

Kaka,
Hii algebra ina equation moja tu, nevertheless ina unknown moja tu vilevile.

Manipulation zimo but under above scenario. Where can 2nd equation generated from 1st without be the same!!!

 

[NingaR]

Kaka sidhani kama umeona kuwa kuna tofauti kubwa sana kati ya eqn 1 na 2...biiiiig difference...angalia vizuri mkuu..

Alafu pia,njia ya kuchora graph ingefaa pia..
Let 2^x=2x=y
Unachora graph 2 za y
Y=2^x....eqn 1
Na graph ya pili
Y=2x...eqn 2

Hizo graph mbili zinapointersect unapata value za y alafu unaweka kwenye equation yeyote kupata x..mchezo kwisha

graphical method ndio pekee itakayo leta majibu bila ubishi

 

[Mugizi1]

Twende kazi: 2^x=2x
log2^x=log2x
xlog2=log2+logx
xlog2-log2=logx
log2[x-1]=logx dividing by
log2[x-1] throughout we have
1=logx/log2[x-1]
1=logx base 2[x-1] in exp form it is 2[x-1]^1=2(x-1)=x
2x-2=x
x=2 kwishney

 

[Shakir]

ooh yeah....achana na yale ya kule....mi niko single and fresh.....najua wananzi hawawezi kuja hapa kwenye hesabu.....wewe usiwe na wasiwasi......

Eti eee??
Kweli aisee ukitaka kumfichia kitu Mtanzania muwekee kwenye kitabu, huku hawawezi kuja wale wanoko!!
Za A-Town?

 

[Shakir]

graphical method ndio pekee itakayo leta majibu bila ubishi

Mbona unaniruka tena??
Si tulikubaliana "trial & error" inahusika hapa mkuu wangu??