Jibu ni 2, tatizo ni njia

[fortunho]

njia;let y=2x....1.then y=2^x....2.then solve graphically utapata intersections mbili then majibu ya x utayapata other wise hutoki

 

[fortunho]

kijana umenofurahisha sana!!
swali kama hilo lazima utumie graphical method ndo peekeyake italeta jibu.
Anza hivi
2^x=2x
=>2^x-2x=0
hapa functionaly itakua hivi
f(x)=2^x-2x
let f(x)=y
utakua
y=2^x-2x
then make table of values kuanzia x=-4,-3,-2,-1,0,1,2,3na4
then chora graph of y=2^x-2x
kumbuka kua y=f(x)=0
then angalia katika graph yako thamani za x wakati y=0
utaona ziko 2 ambazo n
x=1
x=2
:-X=1 and X=2

natumai umeelewa

wonderfully

 

[Shark]

wonderfully

Yake ina equation moja,
Yako ina equations mbili!!
Kujua hesabu raha sana, unacheza nazo utakavyo,
Wengine wanasema HAKUNA NJIA,
Wengine wanato njia mbilimbili.
Very interesting!!

 

[NingaR]

Kaka,
Hili swali ni modification tu ya maswali ya log ya kawaida.
Mfano lingeweza kua kama ifuatavyo, na nadhani mtoa swali ametoholea humu.
2^x = x^2
Log (2^x) = Log (x^2)
xlog2 = 2logx
x/logx = 2/log
x=2

Nimetoa mfano tu.
Point yangu ni kua kama the above inewezekana, basi hata 2^x = 2x can also be possible.


Sidhani kama kuna hesabu ambayo haipo popote duniani, kwamba haipo kwenye topic yoyote, sidhani.

Maana kujua tu kwamba x =1 or 2 means ni valid question.

Mkuu hapo kwenye red naomba unieleze kwa nini
LHS umegawa kwa logx na RHS umegawa kwa log

 

[NingaR]

Yake ina equation moja,
Yako ina equations mbili!!
Kujua hesabu raha sana, unacheza nazo utakavyo,
Wengine wanasema HAKUNA NJIA,
Wengine wanato njia mbilimbili.
Very interesting!!

Hiyo ndo Rah ya hesabu bhana, swali moja njia nyiingi.

 

[Shark]

Mkuu hapo kwenye red naomba unieleze kwa nini
LHS umegawa kwa logx na RHS umegawa kwa log

2 imesahaulika RHS, "auto-editing" ilifanya kazi yake supposed to be 2/log2

Inapatikana kwa kuzidisha kwa 1/(log2.logx) both sides

 

[b5-click]

...we unataka jibu lije 2 tu, hata 1 pia ni jibu.!
Ok let's g0..!
SOLN...
Fr0m the Qn...
2^x=2x
...Apply log (base10) both sides.!

xlog2=log2+logx

xlog2-log2 = logx

log2(x-1) = logx

Cancell log, since both are log(base10)

2(x-1) = x

2x-2 = x

2x-x = 2

x = 2.!
...duh.!

 

[NingaR]

...we unataka jibu lije 2 tu, hata 1 pia ni jibu.!
Ok let's g0..!
SOLN...
Fr0m the Qn...
2^x=2x
...Apply log (base10) both sides.!

xlog2=log2+logx

xlog2-log2 = logx

log2(x-1) = logx

Cancell log, since both are log(base10)

2(x-1) = x

2x-2 = x

2x-x = 2

x = 2.!
...duh.!

mkubwa umekosea uki factor log2 out unapata (x-1)log2 sio log2(x-1) hii ni kitu tofauti kabisaaaa

 

[Shark]

mkubwa umekosea uki factor log2 out unapata (x-1)log2 sio log2(x-1) hii ni kitu tofauti kabisaaaa

Sure!!

 

[fortunho]

...we unataka jibu lije 2 tu, hata 1 pia ni jibu.!
Ok let's g0..!
SOLN...
Fr0m the Qn...
2^x=2x
...Apply log (base10) both sides.!

xlog2=log2+logx

xlog2-log2 = logx

log2(x-1) = logx

Cancell log, since both are log(base10)

2(x-1) = x

2x-2 = x

2x-x = 2

x = 2.!
...duh.!

ulikimbia log form two nn.kasome sheria za log upya

 

[fortunho]

Aply log on both side

Xlog2=log2+logx
Xlog2-log2=logx
log2(x-1)=logx
Aya endelea sasa

kilaza

 

[fortunho]

hapo ni Trial and Error method jibu ni 2 or 1

kilaza

 

[fortunho]

toka nianze kusoma Mathematics sijawahi kutana na swali la mtindo huu yaani power ni function pia vilevile function iko katika terms, hapo mzee wacha niingie chimbo kwanza

haya sasa

 

[fortunho]

yap.hapo unacancell log base 10
unabaki na 2(x-1)=x
2x-2=x
2x-x=2
x=2

unakubali kilahisi 2.bam 4 real

 

[NingaR]

haya sasa

pitia thread nzima utaona lilivyo be solved

 

[Loyal_Merchant]

Nigar R naona ndio njia, ama unaweza imodify njia ya Nigar R kwa kusolve simultaneous equation graphicaly. nayo inaenda hivi.

2^x=y................(i)
2x=y..................(ii)

then tumia graphical method kusolve simultaneous equations. na soma point za interception kati ya line ya equation ya kwanza na ya pili then you are done.

 

[QUALIFIED]

Duuuuu!! sasa nimegundua kwanini mwalimu wangu hakunifundisha njia hiyo kwahiyo mzee hapo ni mwendo wa kutest tu ikikataa unatupa kule itakayo kubali unachukua?? sasa hiyo njia hata mtoto wa form two si anaweza itumia?? kweli elimu haina mwisho nimeamini.
naomba nikuulize swali:
HIYO NJIA INAKUBALIKA NA NECTA???

watapitisha mistari miwili al-maarufu kama HIGH WAY...

 

[NingaR]

watapitisha mistari miwili al-maarufu kama HIGH WAY...

eti umpelekee engineer umetumia hicho kinjia anaweza ua mtu.

 

[Mahesabu]

nyie bishaneni mimi mwenye jina nimetulia tu!

 

[QUALIFIED]

eti umpelekee engineer umetumia hicho kinjia anaweza ua mtu.

kha kha kha