$5^{2x}=125$ tenglamani yeching.
- A. $\frac{3}{2}$
- B. $3$
- C. $1$
- D. $2$
Daraja va uning xossalari, darajali ifodalar bo‘yicha savol
Javob va yechimni ko‘rish
Javob: $\frac{3}{2}$
Berilgan tenglama $5^{2x}=125$ dagi asos $5$ ga bir xil bo‘lgani sababli, har ikki tomonning ham logarifmini $5$ asosida olishimiz mumkin:
\[
\log_{5}\!\left(5^{2x}\right)=\log_{5}\!125.
\]
Chap tomonda logarifm $5$ ning darajasiga olib keladi, ya’ni $\log_{5}\!\left(5^{2x}\right)=2x$. O‘ng tomonda $125=5^{3}$ bo‘lgani uchun $\log_{5}\!125=3$. Shunday qilib
\[
2x=3 \;\Longrightarrow\; x=\frac{3}{2}.
\]
Demak, $x$ ning qiymati $\displaystyle \frac{3}{2}$ ga teng. Bu javob variant **A** ga mos keladi.
Mavzuni mustahkamlang
Bu savol Daraja va uning xossalari, darajali ifodalar mavzusiga tegishli. Ta’riflar, formulalar va misollarni mavzu sahifasida ko‘ring.
Mavzuni o‘rganish