The sequence \[\log_{12}{162}, \ \log_{12}{x}, \ \log_{12}{y}, \ \log_{12}{z}, \ \log_{12}{1250}\]is an arithmetic progression. What is $x$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The sequence \[\log_{12}{162}, \ \log_{12}{x}, \ \log_{12}{y}, \ \log_{12}{z}, \ \log_{12}{1250}\]is an arithmetic progression. What is $x$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
270
The sequence \[\log_{12}{162}, \ \log_{12}{x}, \ \log_{12}{y}, \ \log_{12}{z}, \ \log_{12}{1250}\]is an arithmetic progression. What is $x$?
train