How to make global exception filter log errors

Question

I've just created a global exception filter as per Nest's docs, here it is:

import {
  ExceptionFilter,
  Catch,
  ArgumentsHost,
  HttpException,
  HttpStatus,
} from '@nestjs/common';
import { HttpAdapterHost } from '@nestjs/core';

@Catch()
export class GlobalExceptionsFilter implements ExceptionFilter {
  constructor(private readonly httpAdapterHost: HttpAdapterHost) {}

  catch(exception: unknown, host: ArgumentsHost): void {
    const { httpAdapter } = this.httpAdapterHost;

    const ctx = host.switchToHttp();

    const httpStatus =
      exception instanceof HttpException
        ? exception.getStatus()
        : HttpStatus.INTERNAL_SERVER_ERROR;

    const responseBody = {
      statusCode: httpStatus,
      timestamp: new Date().toISOString(),
      path: httpAdapter.getRequestUrl(ctx.getRequest()),
    };

    httpAdapter.reply(ctx.getResponse(), responseBody, httpStatus);
  }
}

And it is now catching every exception, but it's also not logging any errors to the console anymore... My question is both how to do it and should I log every error inside my filter?