Final answer:
To simplify the expression loge - loge⁷ - loge², substitute the values of each term and perform the subtraction. The simplified expression is -6.
Step-by-step explanation:
To simplify the expression loge - loge⁷ - loge², we can use the properties of logarithms. First, let's break down each term:
loge = 1 (since loge x = 1 for any positive x)
loge⁷ = loge(7) = loge(10^7) = 7 (since loge(x^y) = yloge(x))
loge² = (loge)^2 = 1^2 = 1
Now, substitute these values back into the expression:
1 - 7 - 1
Next, perform the subtraction:
1 - 7 - 1 = -6
Therefore, the simplified expression is -6.