Question

Write the expression as a single natural logarithm;
3 ln 3 + 2 ln x

Answer 1

`3 ln(3) + 2ln(x) = ln(27 {x}^(2) )`

EXPLANATION

The given logarithmic expression is

`3 ln(3) + 2ln(x)`

Recall and apply the power rule:

`k \: ln(a) = ln( {a}^(k) )`

`3 ln(3) + 2ln(x) = ln( {3}^(3) ) + ln( {x}^(2) )`

`3 ln(3) + 2ln(x) = ln(27) + ln( {x}^(2) )`

Apply the product rule:

`ln(ab) = ln(a) + ln(b)`

`3 ln(3) + 2ln(x) = ln(27 {x}^(2) )`

Answer 2

ln (27 x²)

Explanation:

Given in the question an expression

3 ln 3 + 2 ln x

Step1

Apply power rule

`mlnx=lnx^(m)`

ln 3³ + ln x²

Step2

Apply multiplication rule

`lnx + lny=ln(xy)`

ln (3³ . x²)

3³ = 27

so

ln (27x²)