$2^a=31$, $3^b=244$ va $5^c=624$ bo'lsa, $a$, $b$, $c$ sonlarini o'sish tartibida joylashtiring.
- A. c<b<a
- B. a<b<c
- C. a<c<b
- D. c<a<b
Daraja va uning xossalari, darajali ifodalar bo‘yicha savol
Javob va yechimni ko‘rish
Javob: c<a<b
Berilgan tenglamalardan $a,b,c$ ning taxminiy qiymatlarini topish uchun har bir asosning birinchi bir necha darajalarini hisoblaymiz.
$2^4=16$, $2^5=32$ → $2^a=31$ ga yaqin qiymat $2^5$ ga, shuning uchun $a\approx5$;
$3^4=81$, $3^5=243$, $3^6=729$ → $3^b=244$ $3^5$ ga juda yaqin, demak $b\approx5$;
$5^3=125$, $5^4=625$ → $5^c=624$ $5^4$ ga deyarli teng, shuning uchun $c\approx4$.
Demak $c$ eng kichik, $a$ va $b$ esa $c$ dan katta, $a<b$ emas, chunki $2^5=32$ $3^5=243$ ga nisbatan kichikroq, shuning uchun $a<b$; natijada $c<a<b$.
Shunday qilib to‘g‘ri javob **D) $c<a<b$**.
Mavzuni mustahkamlang
Bu savol Daraja va uning xossalari, darajali ifodalar mavzusiga tegishli. Ta’riflar, formulalar va misollarni mavzu sahifasida ko‘ring.
Mavzuni o‘rganish