Maths Questions ! Fast PLz~－飛航百科

標題:

Maths Questions ! Fast PLz~

發問:

1) 3^x+1 + 3^x - 108 = 0 2) 6^-2x - (2^2-x)(3^2-x) = 0 3)3^10a+7 - 27^5a-1 = 0 4)( [m^-1n)^2(mn^-2)^-2 ] / m^-3n^-4 5) [ (2^n+1) + 5 (2^n ) ] / 49( 2 ^-n ) 6) (80 000 000 * 0. 000 0005) / 0.00002 7) ( 0.49 * 10^-5) / ( 700*10 ^ -20)

最佳解答:

1) 3^(x+1) + 3^x - 108 = 0 3*3^x + 3^x = 108 (3 + 1)*3^x = 108 4*3^x = 108 3^x = 27 3^x = 3^3 x = 3 ===== 2) 6^-2x - [2^(2-x)] [3^(2-x)] = 0 6^-2x - 6^(2-x) = 0 6^-2x = 6^(2-x) -2x = 2 - x x = -2 ===== 3) 3^(10a+7) - 27^(5a-1) = 0 3^(10a+7) - (3^3)^(5a-1) = 0 3^(10a+7) - 3^(15a-3) = 0 3^(10a+7) = 3^(15a-3) 10a + 7 = 15a - 3 5a = 10 a = 2 ===== 4) [(m^-1 n)^2 (m n^-2)^-2 ] / (m^-3 n^-4) = [(m^-2 n^2) (m^-2 n^4)] / (m^-3 n^-4) = m^[(-2)+(-2)-(-3)] n^[2+4-(-4)] = m^-1 n^10 = n^10 / m ===== 5) [(2^(n+1)) + 5(2^n)] / 49(2^-n ) = (2*2^n + 5*2^n) / 49*2^-n = (2 + 5)*2^n / 49*2^-n = (7/49)*2^[n-(-n)] = 2^2n / 7 ===== 6) (80 000 000 * 0. 000 0005) / 0.00002 = (8 * 10^7) * (5 * 10^-7) / (2 * 10^-5) = (8*5/2) * 10^[7+(-7)-(-5)] = 20 * 10^5 = 2 000 000 ===== 7) ( 0.49 * 10^-5) / ( 700 * 10^-20) = (4.9 * 10^-6) / (7 * 10^-18) = (4.9/7) * 10[(-6)-(-18)] = 0.7 * 10^12 = 7 * 10^11

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