设log(2)(3)=a,log(3)(7)=b,以a,b表示log(21)(56)
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设log(2)(3)=a,log(3)(7)=b,以a,b表示log(21)(56)
利用对数换底公式:
log(21)(56) = (ln56)/(ln21) = [ln8 + ln7]/[ln3 + ln7]
= [3ln2 + ln7]/[ln3 + ln7]
= [3(ln2)/(ln3) + (ln7)/(ln3)] / [1 + (ln7)/(ln3)]
∵a = log(2)(3) = (ln3)/(ln2) ,b = log(3)(7) = (ln7)/(ln3)
∴log(21)(56) = [(3/a) + b] / [1 + b]
= (ab + 3) / (ab + a)
log(21)(56) = (ln56)/(ln21) = [ln8 + ln7]/[ln3 + ln7]
= [3ln2 + ln7]/[ln3 + ln7]
= [3(ln2)/(ln3) + (ln7)/(ln3)] / [1 + (ln7)/(ln3)]
∵a = log(2)(3) = (ln3)/(ln2) ,b = log(3)(7) = (ln7)/(ln3)
∴log(21)(56) = [(3/a) + b] / [1 + b]
= (ab + 3) / (ab + a)
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