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[中四]對數函數

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對數函數有D問題唔識做,大家可唔可以幫下手,如果覺得多就一人做一題解la 題目:http://imagehost.bizhat.com/users/4032/9652___.jpg 更新: 注意:叫我理解左之後就自己做同埋叫我用計數機計果D唔該唔好回

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最佳解答:

1. log 2 + log 5 = log (2*5) = log 10 = 1 2. 3 log 2 + log 125 = log (23) + log 125 = log (23*125) = log (1000) = 3 3. (log 32)/(log 4) = (log 2^5)/(log 22) = (5 log 2)/(2 log 2) = 5/2 4. log 1 * log 7 = 0 * log 7 = 0 5. (log 3√3)/(log 3) = (log 3^(1/3))/(log 3) = 1/3* log 3 / log 3 = 1/3 6. 2 log x + log (1/x2) = log x2 + log (1/x2) = log (x2 * 1/x2) = log 1 = 0 7. log √16 + log √325 - log √52 = log (√16 * √325 / √52) = log √(16*325/52) = log √100 = log 10 = 1 14a. log_4 (12) + log_4 (9) - log_4 (108) = log_4 (12*9/108) = log_4 (1) = 0 14b. log 36 / log 216 = log 62 / log 63 = (3 log 6)/(2 log 6) = 3/2 14c. log_a [^5√(a^3)] + log_a [^4√(a^5)] = log_a [a^(3/5)] + log_a [a^(5/4)] = 3/5 + 5/4 = 37/20 14d. [log_2 (6) + log_2 (3)]/[log_2 (36) + log_2 (9)] = [log_2 (6*3)]/[log_2 (36*9)] = log_2 (18) / log_2 (324) = log_2 (18) / log_2 (182) = log_2 (18) / [2 log_2 (18)] = 1/2 其實最重要的就是要知道對數的公式： 1. log a + log b = log (a*b) 2. log a - log b = log (a/b) 3. log m^n = n log m 4. log_a (a^n) = n 記熟了這些後，其他的都不太難了。 希望幫倒你！ ^^

其他解答:

(1) log 2+log 5 =log (2．5) =log 10 =1 (2) 3 log 2+log 125 =log (2^3)+log 125 =log 8+log 125 =log (8．125) =log 1000 =3 (3) log 32 / log 4 =log (2^5) / log (2^2) =5 log 2 / 2 log 2 =5/2 (4) log 1．log 7 =0．log 7 =0 (5) log [(3)^(1/3)]/log 3 =log 3/3 log 3 =1/3 (6) 2 log x+log (1/x^2) =2 log x+log [x^(-2)] =2 log x-2 log x =0 (7) log [(16)^(1/2)]+log [325^(1/2)]-log [52^(1/2)] =log (16．325 / 52) /2 =log 100 /2 =2/2 =1 (14) 底為a時以log_a 表示 (a) log_4 (12)+log_4 (9) - log_4 (108) =log_4 (12．9 / 108) =log_4 (1) =0 (b) log 36/ log 216 =log (6^2) / log (6^3) =2 log 6 / 3 log 6 =2/3 (c) log_a [a^(3/5)+a^(5/4)] =log_a [a^(3/5+5/4)] =log_a [a^(37/20)] =37(log _a a)/20 =37/20 (d) [log_2 (6)+log_2 (3)]/[log_2 (36)+log_2 (9)] =log_2 (6+3) / log_2 (36+9) =log_2 (9) / log_2 (45) =log_2 (9) / [log_2 (5)+log_2 (9)]|||||1. log2 + log5 = log(2x5) = log 10 = 1 2. 3log2 + log125 = log (3^2) + log 125 = log 8 + log 125 = log (8 x 125) = log 1000 = 3 3. log 32 / log 4 = log (2^5) / log (2^2) = (5log2)/(2log2) = 5/2 4. log 1 x log 7 = 0 x log 7 = 0 5. log [cubic root(3)] / log 3 = (1/3) log 3/ log3 = 1/3 6. 2 log x + log (1/x^2) = log x^2 + log (1/x^2) = log [(x^2)(1/x^2)] = log 1 = 0 7. log sqrt(16) + log sqrt(325) - log sqrt(52) = log [sqrt(16) x sqrt(325) / sqrt(52)] = log [sqrt(16 x 325 / 52)] = log sqrt(100) = log 10 = 1|||||1 log 2+log 5 =log (2 x 5) =log 10 =1 2 3 log 2 + log 125 =3 log 2 +log (5^3) =3 log 2 + 3 log 5 =3(log 2 +log 5) =3(log(2 x 5) =3 x log 10 =3 x 1 =3 3 log 32 / log 4 =log (2^5)/log(2^2) =5log 2 / 2log 2 =5/2 =2.5 4 log1 x log 7 =0 x log 7 =0 5 log cube root(3) / log3 = [1/3 (log3)]/log 3 =(1/3)/1 =1/3 6 2 log x + log (1/x2) =2 log x + (1/2) log x =log x (2+ 1/2) =(5 log x)/2 7 log√16 + log√325- log√52 =log(√16 x √325 / √52) =log √100 =log 10 =1 14a log(4)12+log(4)9-log(4)108 =log(4) x (12 x9 /108) =log(4) 1 =0 14b log36 / log 216 =log(6^2) / log(6^3) =2 log6 / 3 log 6 =2/3 14c 原式 =log(a) a^(3/5) +log(a) a^(5/4) =log a^(3/5) / log a +log a^(5/4) / log a = 3/5 log a / log a + 5/4 log a /log a =3/5 +5/4 =1.85 14d log(2) 6 +log(2) 3 / log(2) 36 +log(2) 9 = [(log 6 +log 3)/log 2] / [(log 36 + log 9)/log 2) =(log 18 / log 2 ) / [(log 324) / log 2] =log 18 / log 324 =log 18 / 2 log 18 =1/2 =0.5A215E4A2B88AAE64