We can use the following basic properties of logarithms to solve logarithmic equations.
Product Rule :
Quotient Rule :
Power Rule :
In each case, find the value of x.
Example 1 :
Solution :
Example 2 :
Solution :
7x  4 = 5(x + 2)
7x  4 = 5x + 10
2x = 14
x = 7
Example 3 :
Solution :
x  2 = 4(x  5)
x  2 = 4x  20
3x = 18
x = 6
Example 4 :
Solution :
x + 1 = x^{2}  82x + 1681
x^{2}  83x + 1680 = 0
Solve by using quadratic formula.
x = 35 or 48
The aruguments of logarithms are always positive or greater than zero.


The common solution of the inequalities x > 0 and x > 40 is
x > 40
Since x > 40, the solution x = 35 can not be acccepted.
Therefore,
x = 48
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