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首先,我们需要计算 f(1) 的值。
f(1) = log2[(3m-6)(1)+2m-5]
= log2[(3m-6+2m-5)]
= log2[5m-11]
log2[5m-11] = log2(1/1+m)
将方程中的分数变为整数:
5m-11 = 1/(1+m)
= 1/(1+m) * (1-m)/(1-m) (分子分母同时乘以 1-m)
= (1-m)/(1+m-m^2) 将得到的结果代入方程中:
5m-11 = (1-m)/(1+m-m^2)
通过移项和整理,得到方程:
(5m-11)(1+m-m^2) = 1-m
将方程进行展开和整理:
5m+5m^2-11-11m+11m^2 = 1-m
合并同类项:
16m^2-6m-12 = 0
再次整理得到:
8m^2-3m-6 = 0
咨询记录 · 回答于2024-01-13
22.已知函数 f(x)=log2[(3m-6)x+2m-5] ,g(x)=log2(1/x+m) mR.-|||-(1)若 f(1)
首先,我们要计算 f(1) 的值。
f(1) = log2[(3m-6)(1)+2m-5]
= log2[(3m-6+2m-5)]
= log2[5m-11]
log2[5m-11] = log2(1/1+m)
5m-11 = 1/(1+m)
将方程中的分数变为整数:5m-11 = 1/(1+m)
= 1/(1+m) * (1-m)/(1-m) (分子分母同时乘以 1-m)
= (1-m)/(1+m-m^2) 将得到的结果代入方程中:5m-11 = (1-m)/(1+m-m^2)
通过移项和整理,得到方程:(5m-11)(1+m-m^2) = 1-m
将方程进行展开和整理:5m+5m^2-11-11m+11m^2 = 1-m
合并同类项:16m^2-6m-12 = 0
再次整理得到:8m^2-3m-6 = 0
所以方程的解为 m = (3+√201)/16 或 m = (3-√201)/16 。这是方程 f(1) = g(1) 的解。