LOGARITHMIC EQUATIONS - 1

If  Log₅x  + log₅(8x+39) = 1; find x

solution

Log₅ [ x(8x+39) ]= 1                        Logarithm of aproduct

[ x(8x+39) ]= 5¹                               Changing it to exponential form

8x² + 39x = 5                                   opening the brackets

8x² + 39x – 5 = 0                             forming a quadratic equation.

8x² + 40x – x –5 = 0                        factorize by splitting the middle term

(8x² + 40x) – (x –5) = 0                  grouping

8x(x + 5) -1(x + 5) = 0                     factorizing

(8x – 1)(x + 5) = 0

8x – 1 = 0 or x + 5 = 0

8x = 1  or  x = -5

8x = 1   or  x = -5

8      8 

X = 1/8  or x = -5     answer