When the game runs on device it will write a log file. This is where your Debug.Log messages will go, together with any asserts, information and error messages from Unity. You can fetch this log from the device from the editor. Use Edit->Project Settings->Player->Publishing Settings->Get Log. The log can be written to the hard drive of your computer. An example log file is:
Set current directory to /accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc
Found path: /accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/com.unity.doc.testDev_ProductName5a2477fc
Data folder: /accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/app/native/Data
Loading in pref's!
Mono path[0] = '/accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/app/native/Data/Managed'
Mono config path = '/accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/app/native/Data/Managed'
Renderer: Adreno (TM) 225
Vendor: Qualcomm
Version: OpenGL ES 2.0 2644020
GL_AMD_compressed_ATC_texture GL_AMD_performance_monitor GL_AMD_program_binary_Z400 GL_EXT_robustness GL_EXT_texture_format_BGRA8888
GL_EXT_texture_type_2_10_10_10_REV GL_NV_fence GL_OES_compressed_ETC1_RGB8_texture GL_OES_depth_texture GL_OES_depth24 GL_OES_EGL_image
GL_OES_EGL_image_external GL_OES_element_index_uint GL_OES_fbo_render_mipmap GL_OES_fragment_precision_high GL_OES_get_program_binary
GL_OES_packed_depth_stencil GL_OES_rgb8_rgba8 GL_OES_standard_derivatives GL_OES_texture_3D GL_OES_texture_float GL_OES_texture_half_float
GL_OES_texture_half_float_linear GL_OES_texture_npot GL_OES_vertex_half_float GL_OES_vertex_type_10_10_10_2 GL_OES_vertex_array_object
GL_QCOM_alpha_test GL_QCOM_binning_control GL_QCOM_driver_control GL_QCOM_perfmon_global_mode GL_QCOM_extended_get GL_QCOM_extended_get2
GL_QCOM_tiled_rendering GL_QCOM_writeonly_rendering GL_AMD_compressed_3DC_texture GL_EXT_sRGB GL_EXT_texture_filter_anisotropic
GL_ANGLE_framebuffer_multisample GL_ANGLE_framebuffer_blit GL_OES_mapbuffer
Creating OpenGLES2.0 graphics device
Initialize engine version: 4.2.0a1 (20a94a2c4d7f)
Begin MonoManager ReloadAssembly
Platform assembly: /accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/app/native/Data/Managed/UnityEngine.dll (this message is harmless)
Loading /accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/app/native/Data/Managed/UnityEngine.dll into Unity Child Domain
Platform assembly: /accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/app/native/Data/Managed/Assembly-CSharp.dll (this message is harmless)
Loading /accounts/1000/appdata/com.unity.doc.testDev_ProductName5a2477fc/app/native/Data/Managed/Assembly-CSharp.dll into Unity Child Domain
- Completed reload, in 0.129 seconds