1.已知log以10為底的2=0.3010、log以10為底

1.
log10 36
= log10 (4 x 9)
= log10 (2² x 3²)
= log10 (2 x 3)²
= 2 log10 (2 x 3)
= 2 x (log10 2 + log10 3)
= 2 x (0.3010 + 0.4771)
= 1.5562


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2.
[log2 125 + log8 (1/5)] [log5 2 + log125(1/2)]
= [(log 125 / log 2) + (log 5⁻¹ / log 8)] [(log 2 / log 5)+ (log 2⁻¹ / log 125)]
= [(log 5³ / log 2) + (log 5⁻¹ / log 2³)] [(log 2 / log 5) + (log2⁻¹ / log 5³)]
= [(3log 5 / log 2) - (log 5 / 3 log 2)] [(log 2 / log 5) - (log 2 / 3 log 5)]
= [ (9 log 5 - log 5) / 3 log 2] [(3 log 2 - log 2) / 3 log 5]
= [8 log 5 / 3 log 2] [2 log 2 / 3 log 5]
= 16/9


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3.
不能貼圖，此題從略。


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4.
log8(x + 4) + log8 (x - 3) = 1
log8 [(x + 4)(x - 3)] = log88
(x + 4)(x - 3) = 8
x² + x - 12 = 8
x² + x - 20 = 0
(x - 4)(x + 5) = 0
x = 4 或 x = -5 (不合，因負數無對數)

這有類似的

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問樓主是否對log有所了解，這些題目算是基礎喔