Question

Expand the logarithm log3(h/9)
.(1 point)
Responses

log3h − 2
log3h − 2

log3(h − 3)
log3(h − 3)

(h - 2)
(h - 2)

log3h2

Answer 1

To expand the logarithm \( \log_3\left(\frac{h}{9}\right) \), we can use the properties of logarithms, specifically:

1. The quotient rule: \( \log_b\left(\frac{x}{y}\right) = \log_b(x) - \log_b(y) \)
2. The logarithm of a constant: \( \log_b(a) \)

Applying these properties, we have:

\[
\log_3\left(\frac{h}{9}\right) = \log_3(h) - \log_3(9)
\]

Next, we can simplify \( \log_3(9) \). Since \( 9 = 3^2 \), we can write:

\[
\log_3(9) = \log_3(3^2) = 2
\]

Putting this back into the equation:

\[
\log_3\left(\frac{h}{9}\right) = \log_3(h) - 2
\]

Thus, the expanded form of \( \log_3\left(\frac{h}{9}\right) \) is:

\[
\log_3(h) - 2
\]

The correct response is:

**log3h − 2**