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Vlad [161]
3 years ago
9

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

Mathematics
2 answers:
crimeas [40]3 years ago
4 0

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)

Blababa [14]3 years ago
3 0

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} )

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