Natural and Common Log Operations:

The utilization of the log/ln can be seen through trying to solve the subsequent equation algebraically. That equation cannot be solved by algebraic methods.  Here is the mechanism for solving this equation is as given below:

Using Common Logs                                             Using Natural Logs

2x = 7                                                                          2x = 7

Log 2x = log 7                                                            ln 2x = ln 7

X log 2 = log 7                                                            X ln 2 = ln 7

X = log 7/log 2 = 0.8451/0.3010 = 2.808                   X = ln 7/ln 2 = 1.946/0.693 = 2.808

How would you calculate x in the subsequent equation?

log x = 5

The simple way to solve this equation is to take the anti-log. A multiplication reverse is division, so anti-log is the reverse of log.  For take the anti-log log₁₀ x = 5:

anti-log (log X) = anti-log 5

x = anti-log 5

x = 100,000

This is accomplished on a calculator through pressing the 5, INV, then the LOG key.  That causes the inverse of the log process.