meredith48034
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Condense the expression to the logarithm of a single quantity


-4 ln(3x)


Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.)

1. ln (2x)



Answer :

mhanifa

Part 1

Condense the expression:

  • - 4 ln (3x) =
  • ln (3x)⁻⁴

Used property:

  • n logₐ b = logₐ bⁿ

Part 2

Expand the expression:

  • ln (2x) =
  • ln 2 + ln x

Used property:

  • log (ab) = log a + log b
semsee45

Answer:

[tex]\ln(3x)^{-4}[/tex]

[tex]\ln2 + \ln x[/tex]

Step-by-step explanation:

Given expression:

[tex]-4\ln(3x)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\implies \ln(3x)^{-4}[/tex]

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Given expression:

[tex]\ln(2x)[/tex]

[tex]\textsf{Apply the product law}: \quad \ln xy=\ln x + \ln y[/tex]

[tex]\implies \ln2 + \ln x[/tex]

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