a uchun yechish
a=5-b
b uchun yechish
b=5-a
Viktorina
Algebra
{ 3 }^{ a+b } = 243
Baham ko'rish
Klipbordga nusxa olish
3^{a+b}=243
Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.
\log(3^{a+b})=\log(243)
Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.
\left(a+b\right)\log(3)=\log(243)
Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.
a+b=\frac{\log(243)}{\log(3)}
Ikki tarafini \log(3) ga bo‘ling.
a+b=\log_{3}\left(243\right)
Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
a=5-b
Tenglamaning ikkala tarafidan b ni ayirish.
3^{b+a}=243
Tenglamani yechish uchun eksponent va logaritmlarning qoidalaridan foydalanish.
\log(3^{b+a})=\log(243)
Tenglamaning ikkala tarafiga tegishli logaritmni chiqarish.
\left(b+a\right)\log(3)=\log(243)
Darajaga ko'tarigan logaritm raqami raqam logaritmining darajasidir.
b+a=\frac{\log(243)}{\log(3)}
Ikki tarafini \log(3) ga bo‘ling.
b+a=\log_{3}\left(243\right)
Asosiy tenglamani almashtirish orqali \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).
b=5-a
Tenglamaning ikkala tarafidan a ni ayirish.
Misollar
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