Question

If log₁₀(2x + 3) − 1 = log₁₀x, then find x.
1. 3/8
2. 7/8
3. 2/7
4. 3/4

Answer 1

Correct Answer - Option 1 : 3/8

Calculation:

log₁₀(2x + 3) − 1 = log₁₀x
⇒ log₁₀(2x + 3) − log₁₀10 = log₁₀x

⇒ log₁₀((2x + 3)/10) = log₁₀x

⇒ (2x + 3)/10 = x

⇒ 2x + 3 = 10x

⇒ 8x = 3

⇒ x = 3/8

Use these formulas and their vice-versa:

log(p × q) = log(p) + log(q)

log(p/q) = log(p) - log(q)