A logarithmic equation hides the unknown inside a logarithm. The escape route never changes: condense the log side down to a single logarithm, convert that one logarithm into exponential form, then solve what is left. One extra duty comes with the territory — a logarithm refuses negative and zero inputs, so every candidate must be checked in the original equation before you are allowed to call it a solution.
Convert: the whole move in one picture
base b =2.0
right side c =2.0
Why the three rules are true
Where extraneous roots are born
solve log5x + log5(x − 4) = c, c =1.0
Two shapes of log equationchoose one to begin
Worked steps
Substitute a value of x — watch which lines survive it