Solving Logarithmic Equations
Subject:
Calculus [1]
Tags:
Calculus [11]
logarithmic [12]
he first type of logarithmic equation has two?logs, each having the same base, set equal to each other, and you solve by setting the insides (the "arguments") equal to each other. For example: Solve?log2(x) =?log2(14). Since the logarithms on either side of the equation have the same base ("2", in this case), then the only way these two logs can be equal is for their arguments to be equal. In other words, the log expressions being equal says that the arguments must be equal, so I have: x?= 14 And that's the solution:?x?= 14 Solve?logb(x2) =?logb(2x?? 1). Since the bases of the logs are the same (the unknown value "b", in this case), then the insides must be equal. That is: x2?=?2x?? 1 Then I can solve the log equation by?solving this quadratic equation: x2?? 2x?+ 1 = 0