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hello everyone in this video were going to be looking at a logarithmic equation this problem was taken from a book called a problem book in algebra by kretschmar ill share the link down below so we have 2 times the log of x plus 3 equals log of ax and we know that or were told that this equation has only one root and were going to be looking for the a values all right so this is a pretty interesting problem because a is a parameter we dont know what it is thats what were going to find all right so this is the first thing were going to do notice that x plus 3 needs to be greater than 0 in order for this log function to be defined by the way when i say log you should always understand its base 10 otherwise if its base e im going to be writing ln okay so make sure were not confused about that so the first thing im going to do is use the exponent rule so im going to write this as log x plus 3 squared and thats equal to log of ax if you want you can write the x in parenthesis