Question

NO LINKS!!

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 1

`\ln(3x)^(-4)`

`\ln2 + \ln x`

Explanation:

Given expression:

`-4\ln(3x)`

`\textsf{Apply the power law}: \quad n \ln x=\ln x^n`

`\implies \ln(3x)^(-4)`

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Given expression:

`\ln(2x)`

`\textsf{Apply the product law}: \quad \ln xy=\ln x + \ln y`

`\implies \ln2 + \ln x`

Answer 2

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