Expect documentation says:

$object->log_file("filename" | $filehandle | \&coderef | undef)

Log session to a file. All characters send to or received from the spa
+wned process are written to the file. Normally appends to the logfile
+, but you can pass an additional mode of "w" to truncate the file upo
+n open():
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You have

$exp->log_file ("output.log", "w");
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If you remove the second argument ("w"), then it should append to the file. So you can try:

$exp->log_file ("output.log");
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