Question

How can the logarithmic expression be rewritten?

Select True or False for each statement.

Answer 1

Statement 1 : False

Statements 2: True

Statements 3: True

Explanation:

Let's evaluate each statement:

`\sf \log_3 (cd^4) = 4\log_3 c + 4\log_3 d`

• False: The correct formula is:

`\sf \log_b (xy) = \log_b x + \log_b y`, not

`\sf \log_b (x^n) = n\log_b x`

`\sf (3)/(4)(\ln a + \ln b) = \ln \sqrt[4]{a^3b^3}`

• True: This statement is correct. We can use the fact that:

`\sf \ln x^n = n \ln x`.

`\sf 3 \ln e - 2 \ln f = \ln\left((e^3)/(f^2)\right)`

• True: This statement is correct.

We can use the fact that:

`\sf \ln e = 1` and

`\sf \ln (x)/(y) = \ln x - \ln y`