Simplify. Enter the result as a single logarithm with a coefficlent of 1.
\[
\log _{9}\left(9 x^{2}\right)+\log _{9}\left(5 x^{4}\right)=
\]
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Answer
The simplified expression is \(\boxed{\log _{9}\left(45 x^{6}\right)}\)
Step 1 ：The properties of logarithms state that the sum of two logarithms with the same base can be written as a single logarithm where the arguments are multiplied together.
Step 2 ：Therefore, we can combine the two logarithms into one by multiplying the arguments together.
Step 3 ：Let's denote \(x = x\), the base of the logarithm as 9, the first argument of the logarithm as \(9x^{2}\), and the second argument of the logarithm as \(5x^{4}\).
Step 4 ：By combining the two logarithms, we get \(\frac{\log(45x^{6})}{\log(9)}\).
Step 5 ：The simplified expression is \(\boxed{\log _{9}\left(45 x^{6}\right)}\)
