Write the expression as a logarithm of a single expression. $$ \log _{9} 2+\log _{9} 9 k^{2} $$

Question

UpStudy AI · Accepted Answer

To combine the expression $$\log_{9} 2 + \log_{9} 9 k^{2}$$ into a single logarithm, we can use the property of logarithms that states:

$$
\log_b a + \log_b c = \log_b (a \cdot c)
$$

In this case, we have:

$$
\log_{9} 2 + \log_{9} (9 k^{2}) = \log_{9} (2 \cdot (9 k^{2}))
$$

Now, we can simplify the expression inside the logarithm:

$$
2 \cdot (9 k^{2}) = 18 k^{2}
$$

Thus, we can rewrite the original expression as:

$$
\log_{9} 2 + \log_{9} 9 k^{2} = \log_{9} (18 k^{2})
$$

Therefore, the expression as a logarithm of a single expression is:

$$
\log_{9} (18 k^{2})
$$
$$ \log_{9} (18 k^{2}) $$

Write the expression as a logarithm of a single expression. \[ \log _{9} 2+\log _{9} 9 k^{2} \]