Why is it that the rule $$ \log_b(x) \ = \ \frac{\log_c(x)}{\log_c(b)} \ $$ (the logarithm base change rule) is true but $$ \ a \log_b(x) \ = \ \frac{a \log_c(x) }{ a \log_c(b) } \ $$ isn't?
For example why does the equation, $$ \log_{49} 3 \ = \ \frac{\log 49 }{ \log 3 \ } $$ work but $$ \ 4 \log_{49} 3 \ = \ \frac{4 \log 49 }{ 4 \log 3} $$ does not?
All you are doing is multiplying the logarithm by a term, and still multiplying each part by it when "splitting the logarithm up."
P.S. If the answer could be explained in somewhat simple terms it would be appreciated. I'm not like a math major or anything. :)