Question

First use appropriate properties of logarithms to rewrite f(x) and then find f’(x)

Answer 1

• f(x) = 6ln(8) -6ln(x)
• f'(x) = -6/x

Explanation:

You want to rewrite f(x) and differentiate it for f(x) = 6·ln(8/x).

Rules of logarithms

The log of a ratio is the difference of logs:

ln(a/b) = ln(a) -ln(b)

Application

Using this to rewrite f(x), we have ...

f(x) = 6ln(8/x) = 6(ln(8) -ln(x))

f(x) = 6·ln(8) -6·ln(x)

Derivative

The derivative of the constant is zero, so ...

f'(x) = -6/x