Express the following as a single logarithm:

2log₁₀5 - log₁₀2 + 3log₁₀4 + 1

Given,

⇒ 2log₁₀5 - log₁₀2 + 3log₁₀4 + 1

⇒ log₁₀5² - log₁₀2 + log₁₀4³ + log₁₀10

⇒ log₁₀25 + log₁₀64 + log₁₀10 - log₁₀2

⇒ log₁₀$\dfrac{25 \times 64 \times 10}{2}$

⇒ log₁₀$\dfrac{16000}{2} = \text{log}_{10}8000$.

Hence, 2log₁₀5 - log₁₀2 + 3log₁₀4 + 1 = log₁₀8000.