Question

Diketahui :
P = ¹² log 18
Q = ²⁴ log 54
Tentukan P × Q + 5 ( P-Q)



tolong banget bantu kak ,urgent​

Answer 1

Jawab:

Penjelasan dengan langkah-langkah:

Diketahui:

P = ¹² log 18

Q = ²⁴ log 54

Untuk menghitung P × Q + 5 ( P-Q), kita perlu menghitung P dan Q terlebih dahulu.

P = ¹² log 18

= log 18 / log 12

= log (2 * 9) / log 3 * 2^2

= (log 2 + log 9) / (log 3 + 2 log 2)

= (1 + 2 log 3) / (log 3 + 2)

= 3 / (log 3 + 2)

Q = ²⁴ log 54

= log 54 / log 24

= log (2 * 27) / log 2^3 * 3

= (log 2 + log 27) / (3 log 2 + log 3)

= (1 + 3 log 3) / (3 + log 3)

= 4 / (3 + log 3)

Sekarang kita dapat menghitung P × Q + 5 ( P-Q) :

P × Q + 5 ( P-Q)

= 3 / (log 3 + 2) * 4 / (3 + log 3) + 5 (3 / (log 3 + 2) - 4 / (3 + log 3))

= 12 / (log 3 + 2)(3 + log 3) + 5 (3(3 + log 3) - 4(log 3 + 2)) / (log 3 + 2)(3 + log 3)

= 12 + 5(9 + 3 log 3 - 4 log 3 - 8) / (log 3 + 2)(3 + log 3)

= 12 + 5(1 + -log 3) / (log 3 + 2)(3 + log 3)

= 12 + 5(1 - log 3) / (log 3 + 2)(3 + log 3)

Untuk menyederhanakan ekspresi di atas, kita dapat menggunakan sifat distributif:

12 + 5(1 - log 3) / (log 3 + 2)(3 + log 3)

= 12 / (log 3 + 2)(3 + log 3) + 5(1 - log 3) / (log 3 + 2)(3 + log 3)

Sekarang kita dapat membagi kedua ruas dengan (log 3 + 2)(3 + log 3):

= (12 + 5(1 - log 3)) / (log 3 + 2)(3 + log 3)

= 12 / (log 3 + 2)(3 + log 3) + 5(1 - log 3) / (log 3 + 2)(3 + log 3)

= 12 / 9 + 5(1 - log 3) / 9

= 12/9 + 5 - 5 log 3 / 9

= 4/3 + 5 - 5 log 3 / 3

= 13/3 - 5 log 3 / 3

= (13 - 5 log 3) / 3

Jadi, P × Q + 5 ( P-Q) = (13 - 5 log 3) / 3.