bilangan log(ab4), log(a3b7), dan log(a6b9) merupakan tiga suku pertama barisan aritmatika. jika suku ke-11 barisan tersebut adalah log(ap), maka p = ... A. 29

Bab Logaritma
Matematika SMA Kelas X

aritmatika
2 x U2 = U1 + U3
2 x log (a³ b⁷) = log (ab⁴) + log (a⁶b⁹)
log (a³ b⁷)² = log (a b⁴ . a⁶ . b⁹)
a³ˣ² . b⁷ˣ² = a¹⁺⁶ . b⁴⁺⁹
a⁶ . b¹⁴ = a⁷ . b¹³
a⁶ b¹⁴ - a⁷ b¹³ = 0
a⁶ b¹³ (b - a) = 0
b - a = 0
b = a

U1 = log (ab⁴) = log (a . a⁴) = log a⁵ = 5 x log a
U2 = log (a³ b⁷) = log (a³ . a⁷) = log a¹⁰ = 10 x log a
beda = U2 - U1 = 10 x log a - 5 log a
beda = 5 log a

U11 = U1 + 10 x beda
U11 = 5 x log a + 10 x 5 log a = log (ap)
5 log a + 50 log a = log (ap)
55 log a = log (ap)
log a⁵⁵ = log (ap)
a⁵⁵ = a . p
p = a⁵⁵ : a
p = a⁵⁵⁻¹
p = a⁵⁴

**jika U11 = log p, maka p = a⁵⁵

log (ab^4), log (a^3.b^7), log (a^6.b^9) = U1, U2, U3
U2 - U1 = U3 - U2
U2 + U2 = U3 + U1
log (a^3.b^7) + log (a^3.b^7) = log (a^6.b^9) + log (ab^4)
log (a^3.b^7)(a^3.b^7) = log (a^6.b^9)(ab^4)
log (a^6.b^14) = log (a^7.b^13)
a^6.b^14 = a^7.b^13
(b^14)/(b^13) = (a^7)/(a^6)
b = a

log (ab^4), log (a^3.b^7), log (a^6.b^9)
= log (a.a^4), log (a^3.a^7), log (a^6.a^9)
= log a^5, log a^10, log a^15
= 5. log a, 10. log a, 15. log a

A = U1 = 5. log a
B = beda = 10. log a - 5. log a = 5. log a
U11 = A + 10B
log a^p = 5. log a + 10 (5. log a)
p. log a = 5. log a + 50. log a
p. log a = 55. log a
p = 55