Question

log (3x + 1) – log (x – 2) = 1.

∴ x = ______

Options

• `-3/2`

• 5

• 4

• 3

Answer 1

∴ x = 3

Explanation:

log(3x + 1) – log(x – 2) = 1

Step 1: Apply the logarithmic rule:

log a − log b = `log (a/b)`

`log((3x + 1)/(x - 2)) = 1`

Step 2: Convert to exponential form:

`(3x + 1)/(x - 2) = 10^1`

`(3x + 1)/(x - 2) = 10`

Step 3: Multiply both sides by x – 2:

3x + 1 = 10(x – 2)

3x + 1 = 10x – 20

Step 4: Simplify:

3x – 10x = –20 – 1

–7x = –21

x = `(-21)/(-7)`

x = 3