Question

Answer the following:

Solve for x, log_x (8x – 3) – log_x 4 = 2

Answer 1

log_x (8x – 3) – log_x 4 = 2

∴ `log_x ((8x - 3)/4)` = 2

∴ x² = `(8x - 3)/4`

∴ 4x² = 8x – 3

∴ 4x² – 8x + 3 = 0

∴ 4x² – 2x – 6x + 3 = 0

∴ 2x(2x – 1) – 3 (2x – 1) = 0

∴ (2x – 1) (2x – 3) = 0

∴ 2x – 1 = 0 or 2x – 3 = 0

∴ x = `1/2` or x = `3/2`