@Test
  public void doesNotChangeApplicationLoggerLogLevel() {
    distributionConfig.setLogLevel(WARNING.intLevel());

    assertThat(applicationLogger.getLevel()).isEqualTo(Level.INFO);
  }
Integration tests for log level control using {@link DistributionConfig} with lifecycle of
{@link Cache}.
geode-core/src/integrationTest/java/org/apache/geode/logging/internal/api/LogLevelChangesWithCacheIntegrationTest.java