Question

If log₁₀x + log₁₀x² = 2 log₁₀x + 1, then what is the value of x?
1. 1
2. 2
3. 5
4. 10

Answer 1

Correct Answer - Option 4 : 10

Given:

log10x + log10x2 = 2 log10x + 1

Formula used:

log a + log b = log ab

bloga = log a^b

Calculation:

log10x + log10x2 = 2 log10x + 1

⇒ log₁₀x³ = log₁₀x² + log₁₀10

⇒ log10x3 = log1010x2

On comparing both sides

x³ = 10x²

⇒ x = 10

∴ The value of x is 10.