Ada yang ngerti nomor 4 dan 5?? Tolong dong
Matematika
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Ada yang ngerti nomor 4 dan 5?? Tolong dong
1 Jawaban
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1. Jawaban bapakdr
^ pangkat
4) 16^x.16¹ - (2²)^x.2^4 = 32
16.(4²)^x - 4^x.16 = 32
16.(4^x)² - 16(4^x) = 32
misalkan 4^x = p
16p² - 16p = 32
16p² - 16p - 32 = 0
--------------------------- ÷ 16
p² - p - 2 = 0
(p - 2)(p + 1) = 0
p = 2 ----> 4^x = 2
p = -1 ----> 4^x = -1 (tidak memenuhi karena pankat hasilnya tidak negatif)
4^(x - 3) = 4^x . 4^-3
= 2 . 1/4^3
= 2/64
= 1/32
5) 6^x.6² + 6¹.6^-x = 30
6^x.36 + 6.(1/6^x) = 30
36.6^x + 6/6^x = 30
misal 6^x = p
36p + 6/p = 30
---------------------- × p
36p² + 6 = 30p
36p² - 30p + 6 = 0
-------------------------- ÷ 6
6p² - 5p + 1 = 0
(3p - 1)(2p - 1) = 0
3p = 1
p = 1/3
6^x = 1/3
x1 = ^6log 1/3
2p = 1
p = 1/2
6^x = 1/2
x2 = ^6log 1/2
x1 + x2 = ^6log 1/3 + ^6log 1/2
= ^6log (1/3×1/2)
= ^6log (1/6)
= ^6log 6^-1
= -1.^6log 6
= -1