AWS API Gateway的执行日志默认是存储在CloudWatch Logs中的，可以通过创建API Gateway时在Stage中配置日志设置来改变日志路径。代码示例如下：

Aws::ApiGateway::RestApi:
  Properties:
    Name: my-api
    Description: My API Gateway
    EndpointConfiguration:
      Types:
        - REGIONAL
    Tags:
      Team: myteam
  Metadata:
    'AWS::CloudFormation::Designer':
      id: 12345
  DeletionPolicy: Retain

# 创建一个API Gateway Stage，并在其中配置日志
Aws::ApiGateway::Deployment:
  Type: AWS::ApiGateway::Deployment
  Properties:
    RestApiId: !Ref MyApi
    StageName: production
    Description: Production deployment
    Variables:
      environment: production
    AccessLogSetting:
      DestinationArn: !Ref AccessLogGroup
      Format: '{"requestId":"$context.requestId","ip":"$context.identity.sourceIp","caller":"$context.identity.caller","user":"$context.identity.user","requestTime":"$context.requestTime","httpMethod":"$context.httpMethod","resourcePath":"$context.resourcePath","status":"$context.status","protocol":"$context.protocol","responseLength":"$context.responseLength"}'

AccessLogGroup:
  Type: 'AWS::Logs::LogGroup'
  Properties:
    LogGroupName: /aws/api-gateway/my-api-logs
    RetentionInDays: 7

该代码会创建一个API Gateway和一个API Gateway Stage，并将日志存储到指定路径的日志组中。可以根据需要更改日志格式、日志组名称等设置。