〔數學〕數學4條

1.化簡(2a^-5/4b^2c)^-2
(2a^-5/4b^2c)^-2
= [2^(-2) * a^(-5)*(-2)]/[4^(-2) * b^2(-2) * c]
= (1/4 * a^10)/[1/16 * b^(-4) * c]
= 4a^10 * b^4 / c
= 4a^10 b^4 /c
2.化簡(3a^-3/5)．(3/a^1/5)^2
(3a^-3/5)．(3/a^1/5)^2
= (3a^-3/5)．[3^(2)/a^2/5]
= 27/a^(3/5 + 2/5)
= 27/a
3.已知f(x)=9(2^x) , g(x)=3(0.5^x) , h(x)=f(x)/g(x)
3a.把h(x)寫成ka^x的形式 b.由此,求h(3)
h(x)=f(x)/g(x)
= 9(2^x)/3(0.5^x)
= 3(2^x)/0.5^x
= 3(2^x)/(1/2)^x
= 3(2^x)/2^(-x)
= 3[2^(x+x)]
= 3(2^2x)
h(3) = 3[2^(2*3)]
= 3(64)
= 192
4.解方程
9^3=9^1-y -------(1)
3^x+y．9^y=9^2x --------(2)
From (1), 27=9-y
y = -18 -------(3)
Sub (3) into(2),
3^x + [-18*9^(-18)] = 9^2(-18)
3^x = 19*9^(-18)
x = log[19*9^(-18)]/log3
x = -33.3 (corr . to 3 sig. fig.)