Use appropriate properties of logarithms to rewrite f(x), and then find
-f(x) = 5x + 4 ln 2x

Question

Use appropriate properties of logarithms to rewrite f(x), and then find 
-f(x) = 5x + 4 ln 2x

Quizplus · Accepted Answer

Using the property that ln(ab) = ln(a) + ln(b), we can rewrite f(x) as: 
f(x) = 5x + 4(ln 2 + ln x)
f(x) = 5x + 4ln 2 + 4ln x
Now, we can use the property that a ln b = ln (b^a) to further simplify: 
f(x) = 5x + ln 2^4 + ln x^4
f(x) = 5x + ln 16 + ln x^4
f(x) = 5x + ln 16x^4
Now, we plug in x = e and evaluate: 
f(e) = 5e + ln 16e^4
f(e) = 5e + ln 16 + ln e^4
f(e) = 5e + ln 16 + 4ln e
f(e) = 5e + ln 16 + 4
f(e) = 5e + ln 16 + 4
f(e) ≈ 22.2
Using a calculator or logarithm tables, we find that ln 16 ≈ 2.77 and ln e ≈ 1. So, f(e) ≈ 22.2. This matches answer choice D.

Use Appropriate Properties of Logarithms to Rewrite F(x), and Then