Question

correctly re write f(x) = log2 (32x^6)

Answer 1

To rewrite the function \( f(x) = \log_2(32x^6) \), we can use the properties of logarithms.

1. **Logarithm of a Product**: \( \log_b(mn) = \log_b m + \log_b n \)
2. **Logarithm of a Power**: \( \log_b(m^n) = n \cdot \log_b m \)

Using these properties, we can rewrite \( f(x) \):

\[
f(x) = \log_2(32x^6) = \log_2(32) + \log_2(x^6)
\]
\[
= \log_2(32) + 6 \cdot \log_2(x)
\]

Next, calculate \( \log_2(32) \). Since \( 32 = 2^5 \):

\[
\log_2(32) = 5
\]

Thus, we plug this back into our equation:

\[
f(x) = 5 + 6 \cdot \log_2(x)
\]

So the rewritten function is:

\[
f(x) = 5 + 6\log_2(x)
\]