1.設1/27=3^n，根號125=5^m，其中m、n為實數

1.
1/27 = 3^n
3^-3 = 3^n
n = -3

125 = 5^m
5^3 = 5^m
m = 3

n + 2m
= (-3) + 2(3)
= 3


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2.
log a = log 0.3^(-3) = -3 log 0.3
log b = log 0.3^(1/5) = (1/5) log 0.3 = 0.2 log 0.3
log c = log 0.3^(1/2) = (1/2) log 0.3 = 0.5 log 0.3

由於 0.5 log0.3 > 0.2 log 0.3 > -3 log 0.3
故此 log c > log b > loga
所以 c > b > a


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3.
不能貼圖，此題從略。


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4.
設兩根為 x = α 及 x = β。

2^(2x + 1) - 9(2^x) + 4 = 0
2(2^2x) - 9(2^x) + 4 = 0
2(2^x)^2 - 9(2^x) + 4 = 0

2^α 及 2^β 為以上方程式的兩根。
兩根之積：(2^α) * (2^β) = 4/2
2^(α + β) = 2^1
α + β = 1