what is the difference between logarithmic function and exponential function
Answers
ʜɪɪ ᴍᴀᴛᴇ ʜᴇʀᴇ's ᴜʀ ᴀɴsᴡᴇʀ....
ᴛʜɪs ᴍᴇᴀɴs ᴛʜᴀᴛ ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ ɪs ᴀɴ ɪɴᴄʀᴇᴀsɪɴɢ ғᴜɴᴄᴛɪᴏɴ. ... ᴛʜᴇ ɪɴᴠᴇʀsᴇ ᴏғ ᴀɴ ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ғᴜɴᴄᴛɪᴏɴ ɪs ᴀ ʟᴏɢᴀʀɪᴛʜᴍɪᴄ ғᴜɴᴄᴛɪᴏɴ ᴀɴᴅ ᴛʜᴇ ɪɴᴠᴇʀsᴇ ᴏғ ᴀ ʟᴏɢᴀʀɪᴛʜᴍɪᴄ ғᴜɴᴄᴛɪᴏɴ ɪs ᴀɴ ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ғᴜɴᴄᴛɪᴏɴ. ɴᴏᴛɪᴄᴇ ᴀʟsᴏ ᴏɴ ᴛʜᴇ ɢʀᴀᴘʜ ᴛʜᴀᴛ ᴀs x ɢᴇᴛs ʟᴀʀɢᴇʀ ᴀɴᴅ ʟᴀʀɢᴇʀ, ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ ᴠᴀʟᴜᴇ ᴏғ ғ(x) ɪs ɪɴᴄʀᴇᴀsɪɴɢ ᴍᴏʀᴇ ᴀɴᴅ ᴍᴏʀᴇ ᴅʀᴀᴍᴀᴛɪᴄᴀʟʟʏ.....
ᴀ ᴇxᴀᴍᴘʟᴇ ...ɪs ᴀᴛᴛᴀᴄʜᴇᴅ...ᴄʜᴇᴄᴋɪᴛ ᴏᴜᴛ.....
ɪɴ ᴛʜɪs sᴇᴄᴛɪᴏɴ ᴡᴇ ᴡɪʟʟ ɪʟʟᴜsᴛʀᴀᴛᴇ, ɪɴᴛᴇʀᴘʀᴇᴛ, ᴀɴᴅ ᴅɪsᴄᴜss ᴛʜᴇ ɢʀᴀᴘʜs ᴏғ ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ᴀɴᴅ ʟᴏɢᴀʀɪᴛʜᴍɪᴄ ғᴜɴᴄᴛɪᴏɴs. ᴡᴇ ᴡɪʟʟ ᴀʟsᴏ ɪʟʟᴜsᴛʀᴀᴛᴇ ʜᴏᴡ ʏᴏᴜ ᴄᴀɴ ᴜsᴇ ɢʀᴀᴘʜs ᴛᴏ ʜᴇʟᴘ ʏᴏᴜ sᴏʟᴠᴇ ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ᴀɴᴅ ʟᴏɢᴀʀɪᴛʜᴍɪᴄ ᴘʀᴏʙʟᴇᴍs ᴀɴᴅ ᴄʜᴇᴄᴋ ʏᴏᴜʀ sᴏʟᴜᴛɪᴏɴs.
ɢʀᴀᴘʜs ᴏғ ғᴜɴᴄᴛɪᴏɴs ɪɴ ɢᴇɴᴇʀᴀʟ:
ʀᴇᴄᴀʟʟ ᴛʜᴀᴛ ɢʀᴀᴘʜs ᴀʀᴇ ᴍᴀᴅᴇ ᴜᴘ ᴏғ ᴘᴏɪɴᴛs ᴛʜᴀᴛ ᴀʀᴇ ᴘʟᴏᴛᴛᴇᴅ ᴏɴ ʀᴇᴄᴛᴀɴɢᴜʟᴀʀ ᴄᴏᴏʀᴅɪɴᴀᴛᴇ sʏsᴛᴇᴍs. ᴛʜᴇ ᴘᴏɪɴᴛs ᴄᴏɴsɪsᴛ ᴏғ ᴛᴡᴏ ᴘᴀʀᴛs: (ɪɴᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ, ᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ). ᴛʜᴇ ᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ ɪs sᴏ ɴᴀᴍᴇᴅ ʙᴇᴄᴀᴜsᴇ ɪᴛ's ᴠᴀʟᴜᴇ ᴀɴᴅ ʙᴇʜᴀᴠɪᴏʀ ᴅᴇᴘᴇɴᴅ ᴏɴ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴀɴᴅ ʙᴇʜᴀᴠɪᴏʀ ᴏғ ᴛʜᴇ ɪɴᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ. ғᴏʀ ᴘᴜʀᴘᴏsᴇs ᴏғ ᴅɪsᴄᴜssɪᴏɴ, ᴡᴇ ᴡɪʟʟ ʀᴇғᴇʀ ᴛᴏ ᴛʜᴇ ɪɴᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ ᴀs x ᴀɴᴅ ᴛʜᴇ ᴅᴇᴘᴇɴᴅᴇɴᴛ ᴠᴀʀɪᴀʙʟᴇ ᴀs ʏ ᴏʀ ғ(x). ɪɴ ʀᴇᴀʟɪᴛʏ, ʏᴏᴜ ᴄᴏᴜʟᴅ ʟᴀʙᴇʟ ᴛʜᴇᴍ ᴀɴʏᴛʜɪɴɢ: (ᴘ, ϙ), (ᴀ, ʙ), (ᴅ, ᴄ), ᴇᴛᴄ.
ʀᴇᴍɪɴᴅᴇʀ: ʀᴇᴍᴇᴍʙᴇʀ ᴛʜᴀᴛ ᴡʜᴇɴ ᴡᴇ ᴛᴀʟᴋ ᴀʙᴏᴜᴛ ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ, ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ ᴠᴀʟᴜᴇ, ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ, ʏ ᴏʀ ғ(x), ᴡᴇ ᴀʀᴇ ᴛᴀʟᴋɪɴɢ ᴀʙᴏᴜᴛ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴀɴᴅ ʙᴇʜᴀᴠɪᴏʀ ᴏғ ᴛʜᴇ ʏ ᴘᴀʀᴛ ᴏғ ᴛʜᴇ ᴘᴏɪɴᴛ (x, ʏ) ɪɴ ᴛʜᴇ ғᴜʟʟ sᴇᴛ ᴏғ ᴛʜᴇ ᴘᴏɪɴᴛs ᴛʜᴀᴛ ғᴏʀᴍ ᴛʜᴇ ɢʀᴀᴘʜ..
ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ɢʀᴀᴘʜs:
ᴏɴᴄᴇ ʏᴏᴜ ᴋɴᴏᴡ ᴛʜᴇ sʜᴀᴘᴇ ᴏғ ᴀɴ ᴇxᴘᴏɴᴇɴᴛɪᴀʟ ɢʀᴀᴘʜ , ʏᴏᴜ ᴄᴀɴ sʜɪғᴛ ɪᴛ ᴠᴇʀᴛɪᴄᴀʟʟʏ ᴏʀ ʜᴏʀɪᴢᴏɴᴛᴀʟʟʏ, sᴛʀᴇᴛᴄʜ ɪᴛ, sʜʀɪɴᴋ ɪᴛ, ʀᴇғʟᴇᴄᴛ ɪᴛ, ᴄʜᴇᴄᴋ ᴀɴsᴡᴇʀs ᴡɪᴛʜ ɪᴛ, ᴀɴᴅ ᴍᴏsᴛ ɪᴍᴘᴏʀᴛᴀɴᴛ ɪɴᴛᴇʀᴘʀᴇᴛ ᴛʜᴇ ɢʀᴀᴘʜ.
ᴇxᴀᴍᴘʟᴇ 1:
ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ ᴛᴇx2ʜᴛᴍʟ_ᴡʀᴀᴘ_ɪɴʟɪɴᴇ18 ɪs ᴀʟᴡᴀʏs ᴘᴏsɪᴛɪᴠᴇ. ᴛʜᴇʀᴇ ɪs sɪᴍᴘʟʏ ɴᴏ ᴠᴀʟᴜᴇ ᴏғ x ᴛʜᴀᴛ ᴡɪʟʟ ᴄᴀᴜsᴇ ᴛʜᴇ ᴠᴀʟᴜᴇ ᴏғ ᴛᴇx2ʜᴛᴍʟ_ᴡʀᴀᴘ_ɪɴʟɪɴᴇ20 ᴛᴏ ʙᴇ ɴᴇɢᴀᴛɪᴠᴇ. ᴡʜᴀᴛ ᴅᴏᴇs ᴛʜɪs ᴍᴇᴀɴ ɪɴ ᴛᴇʀᴍs ᴏғ ᴀ ɢʀᴀᴘʜ? ɪᴛ ᴍᴇᴀɴs ᴛʜᴀᴛ ᴛʜᴇ ᴇɴᴛɪʀᴇ ɢʀᴀᴘʜ ᴏғ ᴛʜᴇ ғᴜɴᴄᴛɪᴏɴ ᴛᴇx2ʜᴛᴍʟ_ᴡʀᴀᴘ_ɪɴʟɪɴᴇ18 ɪs ʟᴏᴄᴀᴛᴇᴅ ɪɴ ϙᴜᴀᴅʀᴀɴᴛs ɪ ᴀɴᴅ ɪɪ.
ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs ʏᴏᴜ...!!...
ᴘʟᴢᴢ ᴍᴀʀᴋ ᴀs ʙʀᴀɪɴʟɪᴇsᴛ.....!!!.......