Question

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

Answer 1

Answer:

ln (27 x²)

Step-by-step 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)

Answer 2

ANSWER

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

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:

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

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