Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with $a \neq 1$ and $b \neq 1$.
\[
2 \log _{5}(5 x+2)+6 \log _{5}(6 x-4)
\]
A. $\log _{5}(5 x+2)^{2}(6 x-4)^{6}$
B. $\log _{5}\left((5 x+2)^{2}+(6 x-4)^{6}\right)$
C. $12 \log _{5}(5 x+2)(6 x-4)$
D. $\log _{5} \frac{(5 x+2) 2}{(6 \sqrt{5}-4) 6}$

Step 1 ：Given the expression \(2 \log _{5}(5 x+2)+6 \log _{5}(6 x-4)\), we need to write it as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with \(a \neq 1\) and \(b \neq 1\).

Step 2 ：The properties of logarithms state that \(n \log_a b = \log_a b^n\) and \(\log_a b + \log_a c = \log_a (b*c)\). Therefore, we can rewrite the expression as a single logarithm by first applying the power rule to each term, and then applying the product rule to combine the two terms into one.

Step 3 ：Applying the power rule, the expression becomes \(\log _{5}(5 x+2)^{2}+\log _{5}(6 x-4)^{6}\).

Step 4 ：Then, applying the product rule, the expression becomes \(\log _{5}(5 x+2)^{2}(6 x-4)^{6}\).

Step 5 ：\(\boxed{\log _{5}(5 x+2)^{2}(6 x-4)^{6}}\) is the expression written as a single logarithm with coefficient 1.