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

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

Answer 2

Answer:

$\ln(3x)^{-4}$

$\ln2 + \ln x$

Step-by-step explanation:

Given expression:

$-4\ln(3x)$

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

$\implies \ln(3x)^{-4}$

---------------------------------------------------------------------------------

Given expression:

$\ln(2x)$

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

$\implies \ln2 + \ln x$