LOGARITHMS 8

If Log₃(2x²- 5x - 3) = 3. Find x.

Solution

Log₃(2x²- 5x - 3) = 3.

 2x²- 5x - 3 = 3³.  [After changing it into exponential form]

2x²- 5x - 3 = 9    since [3³=9]

2x²- 5x – 12= 0

We solve it by factorization;

2x²- 5x – 12= 0

We look for two options m and n such that:

              mn=2x² x (-12) = -24x² and  

              m+n= (-5x)

These have to be -8x and 3x

2x²- 5x – 12= 0

2x²- 8x + 3x – 12= 0

(2x²- 8x) + (3x – 12)= 0

2x(x- 4) + 3(x – 4)= 0

(2x+ 3)(x – 4)= 0

2x+ 3=0 OR x – 4= 0

x=-3/2 or x=4 answer

TRY THIS………………

If Log₉(3x²- 16x + 86) = 2. Find x.