Question

What is \( \log(21x^2) \) written in expanded form?

a) \( 2\log x - \log 21 \)
b) \( \log x - \log 21 + 2 \)
c) \( 2\log 21 - \log x \)
d) \( \log 21 - 2\log x \)

Answer 1

The expanded form of \( \log(21x^2) \) is \( \log(21) + 2\log(x) \), which is not represented by any of the given options.

Step-by-step explanation:

The question asks for the expanded form of \( \log(21x^2) \). According to the properties of logarithms, the logarithm of a product is the sum of the logarithms of the individual factors, and the logarithm of a power allows the exponent to be multiplied by the logarithm of the base. Applying these rules:

\( \log(21x^2) = \log(21) + \log(x^2) \)

Now, using the power rule for logarithms, we can rewrite:

\( \log(x^2) = 2\log(x) \)

So, the expanded form is:

\( \log(21x^2) = \log(21) + 2\log(x) \)

Therefore, none of the given options (a, b, c, d) are correct. The correct expanded form is \( \log(21) + 2\log(x) \).