expand each expression.

$\ln (2x)^4$

$\bigcirc$ $4 \ln 2 + 4 \ln x$
$\bigcirc$ $4 \ln 2 + \ln x$
$\bigcirc$ $8 \ln x$

Question

expand each expression.

$\ln (2x)^4$

$\bigcirc$ $4 \ln 2 + 4 \ln x$
$\bigcirc$ $4 \ln 2 + \ln x$
$\bigcirc$ $8 \ln x$

Accepted Answer

# Explanation:

⚡ Using what you learned: properties of logarithms

## Step 1: Apply the Power Property

$$
\ln((2x)^4) = 4\ln(2x)
$$

## Step 2: Apply the Product Property

$$
4\ln(2x) = 4(\ln 2 + \ln x)
$$

## Step 3: Distribute

$$
4(\ln 2 + \ln x) = 4\ln 2 + 4\ln x
$$

# Answer:

$4\ln 2 + 4\ln x$

Sovi.AI - AI Math Tutor