Mathematics

Express the following as a single logarithm :
2 log₁₀ 5 + 2 log₁₀ 3 − log₁₀ 2 + 1

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Given,

⇒ 2 log₁₀ 5 + 2 log₁₀ 3 − log₁₀ 2 + 1

⇒ log₁₀ 5² + log₁₀ 3² − log₁₀ 2 + 1

⇒ log₁₀ 25 + log₁₀ 9 − log₁₀ 2 + log₁₀ 10

⇒ log₁₀ 25 + log₁₀ 9 + log₁₀ 10 - log₁₀ 2

⇒ log₁₀ (25 × 9 × 10) − log₁₀ 2

⇒ log₁₀ (2250) − log₁₀ 2

⇒ $\log_{10} \space {\Big(\dfrac{2250}{2}\Big)}$

⇒ log₁₀ 1125.

Hence, 2 log₁₀ 5 + 2 log₁₀ 3 − log₁₀ 2 + 1 = log₁₀ 1125.

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