Question

Write the expression as a single natural logarithm.

3 In x - 5 In c.

Answer 1

We'll need two log rules:
Log Exponent Rule: \(\large\rm b\cdot\log(a)=\log(a^b)\)
Log Subtraction to Division Rule: \(\large\rm \log(a)-\log(b)=\log\left(\frac{a}{b}\right)\)

Answer 2

Notice that for the subtraction rule,
there is nothing in front of each log.

So we have to apply our exponent rule first,
to get those things in front out of the way.

Answer 3

Understand how to apply that first rule?
\(\large\rm 3\ln(x)=\ln(x^3)\)
How bout the other term, what do you get?
\(\large\rm 5\ln(c)=?\)