✔ 最佳答案
1)
3²ˣ⁺¹ + 3²ˣ⁻¹ = 8
3²(3²ˣ⁻¹) + 3²ˣ⁻¹ = 8
3²ˣ⁻¹(3² + 1) = 8
3²ˣ⁻¹(10) = 8
log[3²ˣ⁻¹(10)] = log8
log3²ˣ⁻¹ + log10 = log8
(2x - 1)log3 = -1 + log8
2x - 1 = (-1 + log8)/log3
2x = 1 + [(-1 + log8)/log3]
x = (1/2) + [(-1 + log8)/2log3]
x = 0.398
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2)
logy = log(2x) - 1 …… (1)
logx = 2log√(y + 1) …… (2)
(1):
logy = log2x - log10
logy = log(2x/10)
y = 2x/10
x = 5y ….. (3)
(2):
logx = 2log(y + 1)¹ʹ²
logx = (2)(1/2)log(y + 1)
logx = log(y + 1)
x = y + 1 …… (4)
(3) = (4):
5y = y + 1
4y = 1
y = 0.25
Put y = 0.25 into (4):
x = 0.25 + 1
x = 1.25
Hence, x = 1.25, y = 0.25
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3)
3log92 - log954 - log936
= log92³ - log954 - log936
= log98 - log954 - log936
= log8/log9 - log54/log9 - log36/log9
= (log8 - log54 - log36)/log9
= log[8/(54*36)]/log9
= log(1/243)/log9
= -log243/log9
= -log(3)⁵/log(3)²
= -5log3/2log3
= -5/2
= -2.5
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1)
log3(3ˣ⁺¹ - 18) = x
3ˣ⁺¹ - 18 = 3ˣ
3ˣ⁺¹ - 3ˣ = 18
(3)3ˣ - 3ˣ = 18
3ˣ(3 - 1) = 18
3ˣ(2) = 18
3ˣ = 9
3ˣ = 3²
x = 2