If log10 5 + log10 (5x + 1) = log10 (x + 5) + 1, then x is equal to:
Solution
Correct Answer: Option B
⇒ log105 + log10(5x+1) = log10(x+5) + 1
⇒ log105 + log10(5x+1) = log10(x+5) + log1010
⇒ log10[5(5x+1)] = log10[10(x+5)]
⇒ 5(5x+1) = 10(x+5)
⇒ 5x+1 = 2x+10
⇒ 3x = 9
⇒ x = 3
⇒ log105 + log10(5x+1) = log10(x+5) + log1010
⇒ log10[5(5x+1)] = log10[10(x+5)]
⇒ 5(5x+1) = 10(x+5)
⇒ 5x+1 = 2x+10
⇒ 3x = 9
⇒ x = 3
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