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
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.
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!!
Mkuu hapo kwenye red naomba unieleze kwa nini
LHS umegawa kwa logx na RHS umegawa kwa log
...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.!
Sure!!mkubwa umekosea uki factor log2 out unapata (x-1)log2 sio log2(x-1) hii ni kitu tofauti kabisaaaa
...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.!
Aply log on both side
Xlog2=log2+logx
Xlog2-log2=logx
log2(x-1)=logx
Aya endelea sasa
hapo ni Trial and Error method jibu ni 2 or 1
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
yap.hapo unacancell log base 10
unabaki na 2(x-1)=x
2x-2=x
2x-x=2
x=2
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...
eti umpelekee engineer umetumia hicho kinjia anaweza ua mtu.