log3(8x+3) = 1+ log3 (x^2)

We have : log3(8x+3) = 1+ log3
(x^2)

log3(8x+3) = 1+ log3
(x^2)

=> log3(8x+3) - log3 (x^2) =
1

use the property log a - log b = log
(a/b)

=> log3 [(8x + 3)/(x^2)] =
1

=> (8x + 3)/(x^2) =
3

=> 8x + 3 =
3x^3

=> 3x^2 - 8x - 3 =
0

=> 3x^2 - 9x + x - 3 =
0

=> 3x(x - 3) + 1(x - 3) =
0

=> (3x + 1)(x - 3)=
0

=> x = -1/3 and x =
3

Both the values are defined for the logs
given.

The solution of the equation is x =
-1/3 and x = 3