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標題:

Logarithmic Function

發問:

1. Given that log4=x and log24=y, express the following in terms of x and y.(a) log0.06 (b)log32. Given that log2=a and log3=b, express log0.75 in terms of a and b.3. Solve the following logarithmic equations.(a) log(4-3x)=-1(b) log(x-6)-log(x-8)=log2(c) 5^(x-1)=3(x+1)(d) log[x+(1/2)] +... 顯示更多 1. Given that log4=x and log24=y, express the following in terms of x and y. (a) log0.06 (b)log3 2. Given that log2=a and log3=b, express log0.75 in terms of a and b. 3. Solve the following logarithmic equations. (a) log(4-3x)=-1 (b) log(x-6)-log(x-8)=log2 (c) 5^(x-1)=3(x+1) (d) log[x+(1/2)] + log8=log(2x+1)+1

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最佳解答:

1. (a) log(0.06) = log(24 ÷ 4 ÷ 100) = log(24) ? log(4) ? log(100) = x ? y ? 2 (b) log(3) = log(24 ÷ 8) = log(24 ÷ 23) = log(24) ? log(43′2) = log(24) ? (3/2)log(4) = a ? (3/2)b = (2a ? 3b)/2 ==== 2. log(0.75) = log(3 / 4) = log(3 / 22) = log(3) ? log(22) = log(3) ? 2log(2) = b ? 2a ==== 3. (a) log(4 ? 3x) = 1 log(4 ? 3x) = log(10) 4 ? 3x = 10 3x = ?6 x = ?2 (b) log(x ? 6) ? log(x ? 8) = log(2) log[(x ? 6) / (x ? 8)] = log(2) (x ? 6) / (x ? 8) = 2 x ? 6 = 2x ? 16 x = 10 (c) 5??1 = 3??1 log(5??1) = log(3??1) (x ? 1) log(5) = (x + 1) log(3) x log(5) ? log(5) = x log(3) + log(3) x [log(5) ? log(3)] = log(5) + log(3) x = [log(5) + log(3)] / [log(5) ?log(3)] x ≈ 5.301 (d) log[x + (1/2)] + log8 = log(2x + 1) + 1 log[x + (1/2)] + log8 = log(2x + 1) + log(10) log{8[x + (1/2)]} = log[10(2x + 1)] 8[x + (1/2)] = 10(2x + 1) 8x + 4 = 20x + 10 12x = ?6 x = ?1/2 (rejected for log[(?1/2) + (1/2)] is undefined.) Hence, there is no solution. 2015-05-24 00:10:45 補充： 3(d) The last two lines should be : x = ?1/2 (rejected for log[(?1/2) + (1/2)] = log(0) is undefined.) Hence, there is no solution.

其他解答:A9A3995907B431A4