Mathematics
Senior High
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解き方がわかりません

16. 10g23=a, log37 = 6 のとき, 10g 56 をa, b で表せ。

Answers

✨ Best Answer ✨

14=2×7、56=2³×7を利用
また、
log₂7=log₃7/log₃2
   =log₃7/(1/log₂3)
   =log₃7×log₂3
   =ab と置ける

log₁₄56=log₂56/log₂14
=log₂(2³×7)÷log₂(2×7)
={log₂2³+log₂7}÷{log₂2+log₂7}
={3+log₂7}÷{1+log₂7}
=(3+ab)÷(1+ab)
=(3+ab)/(1+ab)

ありがとうございました

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