Easier Way to Simplify log_3 3x?

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To simplify log_3 3x, the solution involves using the logarithmic property that states log_a (yx) = log_a (y) + log_a (x). This leads to the breakdown of log_3 (3x) into log_3 (3) + log_3 (x), resulting in 1 + log_3 (x). While the derivation includes additional steps, they are often unnecessary unless explicitly required for clarity. The consensus is that the straightforward approach is sufficient for most cases. Thus, the simplification of log_3 3x can be efficiently achieved without extensive elaboration.
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hey guys, i have a question, then i will show my solution, is there any chance you guys could help me find an easier way to get to the answer, cheers

question:
log_3 3x

answer:
log_a (yx) = log_a (y) + log_a (x)
log_3 (3) + log_3 (x)
log_a (y) = x -> y = a^x -> log_a (a) = 1 -> y = a^x -> x = 1

1 + log_3 X

is there an easier way of getting to this answer
 
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That is the way to get the answer. You don't need to put the second to last line though in most cases unless you need to write down the rules when you apply them.
 
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