Expand the logarithm log3(h/9)

Question

.(1 point)
Responses

log3h/2
Start Fraction logarithm subscript 3 baseline h over 2 End Fraction

log3h−2
logarithm subscript 3 baseline h minus 2

(h−2)
left parenthesis h minus 2 right parenthesis

log3(h−3)
logarithm subscript 3 baseline left parenthesis h minus 3 right parenthesis

Answer 1

To expand the logarithm \(\log_3\left(\frac{h}{9}\right)\), we can use the logarithmic property that states:

\[ \log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n) \]

In this case, we have \(m = h\) and \(n = 9\). Therefore, we can write:

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

Next, we can simplify \(\log_3(9)\). Since \(9\) can be expressed as \(3^2\), we have:

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

Putting it all together:

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

Thus, the expanded form is:

\[ \log_3(h) - 2 \]

So the correct response from your options is:

log3h−2 (logarithm subscript 3 baseline h minus 2)