標題:
maths
發問:
1.let s=log2 and t =log3,express each of the following in terms of S and t. log1.44^2/3=????? 2.Solve the equation 4^x = 20-4^x+1 3. Solve the equation 2^x = 4^x+1
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最佳解答:
1. log1.442/3 = 2/3 log1.44 = 2/3 log(144 / 100) = 2/3 [log144 – log100] = 2 / 3 log(24 X 32) – 2 / 3 log100 = 2 / 3 [4log2 + 2log3] – 2 / 3 (2) = 8 / 3 log2 + 4 / 3 log3 – 4 / 3 = (8s + 4t – 4) / 3 2. 4x = 20 – 4x+1 4x + 4x+1 = 20 4x + 4 X 4x = 5 X 4 (1 + 4)4x = 5 X 41 4x = 41 x = 1 3. 2x = 4x+1 2x = 22(x + 1) So, x = 2(x + 1) x = -2
其他解答:
1. log1.44^2/3 = 2/3 log1.44 = 2/3 log (2 ^4 x 3^2 x 0.01 ) = 2/3 (log2^4 + log3^2 + log0.01) = 2/3 (4log2 + 2log3 + log0.01)
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